CN111967173A - Method for accurately describing local plastic deformation behavior of metal material - Google Patents
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Abstract
The invention discloses a method for accurately describing local plastic deformation behavior of a metal material. And comparing the measured force with a displacement curve obtained by a uniaxial tensile test, and adjusting a weighting factor and a sub-constitutive equation of a weighted constitutive equation according to the difference of the two curves so that the force and displacement curves of the uniaxial tensile test and finite element simulation are consistent, and the finally adjusted weighted constitutive equation is the constitutive equation method capable of accurately describing local plastic deformation behaviors. The method can accurately describe the local plastic deformation behavior of the metal material, and can be accurately used in finite element simulation to improve the accuracy of the local plastic deformation stage predicted by the finite element simulation, so that the method can be used for guiding the forming process of the metal material.
Description
Technical Field
The invention relates to the technical field of metal materials, in particular to a method for accurately describing local plastic deformation behavior of a metal material.
Background
The stress-strain curve of a material is an important means and method for characterizing the intrinsic properties of the material. The constitutive equation of the material achieves the purpose of predicting the hardening behavior of the material by describing the stress-strain curve of the material. The stress-strain curve of the material comprises an elastic deformation stage and a plastic deformation stage, and the plastic deformation stage is divided into a uniform deformation stage and a local deformation stage. The elastic stage of the material can be accurately described by using Holloman's law, the plastic deformation stage of uniform deformation can also be accurately described by using classical constitutive equations (Hollomon equation, Swift equation or Voce equation), but the local plastic deformation stage (necking stage) is difficult to accurately describe because the true stress-strain curve of the local plastic deformation stage can not be converted by engineering stress-strain according to the volume invariant law, and the constitutive equation capable of accurately describing the local plastic deformation stage is urgently needed in the metal forming process and the damage evolution process in engineering application.
The methods currently described for the local plastic deformation phase mainly use the Bridgman method and finite element iteration. The prediction accuracy and the application range of the Bridgman method are not particularly ideal, and the pure finite element simulation iteration method is too complicated.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a method for accurately describing the local plastic deformation behavior of a metal material, which can accurately describe the local plastic deformation behavior of the metal material and can be accurately used in finite element simulation to improve the accuracy of the local plastic deformation stage predicted by the finite element simulation, thereby being used for guiding the forming process of the metal material. The method can solve the problem that the local plastic deformation of the broken plate cannot be quickly predicted when a forming process engineer forms the metal material.
The technical scheme adopted by the invention is as follows:
a method for accurately describing local plastic deformation behavior of a metal material comprises the following processes:
weighting design is carried out on constitutive equations with different characteristics to obtain weighted constitutive equations;
embedding the weighted constitutive equation into a subprogram of finite element simulation, establishing a finite element model of uniaxial tensile deformation of the metal material, and performing finite element simulation to obtain a force and displacement curve;
comparing the force and displacement curve simulated by the finite element with the force and displacement curve obtained by the uniaxial tensile test, and adjusting the weighting factor and the coefficient of the weighted constitutive equation according to the difference between the force and displacement curve simulated by the finite element and the force and displacement curve obtained by the uniaxial tensile test so that the force and displacement curve simulated by the finite element is consistent with the force and displacement curve obtained by the uniaxial tensile test; and describing local plastic deformation behavior of the metal material by using the weighted constitutive equation at the moment.
Preferably, the weighted constitutive equation is as follows:
σ＝qK(p+0)n+(1-q)f(p)
wherein q is a weighting factor, K is a strength coefficient, n is a strain hardening index,0in order to be pre-strained,pfor plastic strain, σ is true stress, K: (p+0)nIs the principal constitutive equation of Swift, f: (p) Is a sub-constitutive equation, f: (p) According to the strain region of the metal material in the local plastic deformation stage and the uniform deformation stageComparing the two to select;
when the strain interval of the local plastic deformation stage is smaller than the uniform deformation stage, selecting a Voce equation as a secondary constitutive equation; when the strain interval of the local plastic deformation stage is larger than the polynomial equation of the uniform deformation stage, selecting a fourth-order polynomial as a second-order constitutive equation;
wherein, the Voce constitutive equation is as follows:
σ＝σ0-σ0A exp(-βp)
in the formula, σ0For saturation stress, A and beta are Voce equation material coefficients;
the cubic polynomial constitutive equation is:
in the formula, a, b, c, d and e are coefficients of a fourth-order polynomial.
Preferably, when the sub-constitutive equation is Voce constitutive equation, K, n in the weighted constitutive equation,0、σ0The method for obtaining A and beta is as follows:
obtaining an engineering stress-strain curve and a force-displacement curve according to a uniaxial tensile standard test, and converting the engineering stress-strain curve in a uniform deformation stage by using the following formula:
σ＝s(1+e)
＝ln(1+e)
wherein s is engineering stress, e is engineering strain, and e is true strain;
the elastic modulus E is obtained by linear fitting of an elastic stage, and then the elastic modulus E is obtained by processing the data through the-/EpFinally, to σ andpdata utilization of (a ═ K: (a:)p+0)nAnd σ ═ σ -0-σ0A exp(-βp) Fitting to obtain K, n,0、σ0A and beta parameter values.
Preferably, when the second order constitutive equation is a fourth order polynomial, the process of obtaining the initial value of the coefficient of the second order constitutive equation in the weighted constitutive equation is as follows:
according to the necking stage form of the engineering stress-strain curve of the uniaxial tension standard test piece, giving a preliminary curve point of a weighted constitutive equation after necking, wherein the preliminary curve point is represented by sigma K (K)p+0)nAnd the extension curve floats upwards or descends as a reference, then fitting is carried out to obtain a fourth-order polynomial, and the fourth-order polynomial is used as a primary-order constitutive equation.
Preferably, when comparing the force and displacement curve of the finite element simulation with the force and displacement curve obtained by the uniaxial tensile test, the force and displacement curve obtained by the uniaxial tensile test is used as a reference, and the σ ═ σ is0-σ0A exp(-βp) If the force and displacement curve is consistent with the force and displacement curve obtained by the uniaxial tensile test, the quadratic equation is changed into a quadratic polynomial; and for the condition that the quartic polynomial is used as the quartic constitutive equation, adjusting the weighting factor and the quartic polynomial coefficient of the weighted constitutive equation to enable the force and displacement curve of the finite element simulation to be consistent with the force and displacement curve obtained by the uniaxial tensile test.
Preferably, when the weighting factor and the coefficient of the second constitutive equation of the weighting constitutive equation are adjusted:
for σ ═ σ0-σ0A exp(-βp) In the case of a secondary constitutive equation, if a force and displacement curve obtained in a necking stage by finite element simulation is higher than a force and displacement curve obtained in a uniaxial tensile test, the q value is reduced, otherwise, the q value is increased, so that the force and displacement curve simulated by the finite element is consistent with the force and displacement curve obtained in the uniaxial tensile test;
when sigma is sigma0-σ0A exp(-βp) When the force and displacement curve of the finite element simulation necking stage is equivalent to the force and displacement curve obtained by a uniaxial tensile test and is not completely overlapped, the quadratic equation is converted into a fourth polynomial; or, when the quadratic equation is a fourth-order polynomial, the adjustment process is as follows:
firstly, adjusting a quadratic polynomial quadratic equation curve, fitting to obtain a quadratic polynomial coefficient, and repeatedly iterating the fitting process until a force and displacement curve obtained by finite element simulation is consistent with a force and displacement curve obtained by a uniaxial tensile test;
and the weighting constitutive equation formed by the finally adjusted weighting factor q and the coefficient of the secondary constitutive equation is the final weighting constitutive equation, and the final weighting constitutive equation is utilized to describe the local plastic deformation behavior of the metal material.
Preferably, the finite element simulation software is ABAQUS software, and the subroutine of the finite element simulation software is VUMAT.
The invention has the following beneficial effects:
the method determines the final weighted constitutive equation by combining the weighted constitutive equation with a finite element simulation method, and can accurately describe the hardening behavior of the local plastic deformation stage and facilitate the use of engineering personnel, so that the method for accurately describing the local shaping stage can accurately predict the stress, strain and damage evolution of the local shaping stage in the finite element simulation process, thereby more accurately guiding the engineering application. The method can accurately describe the hardening behavior of the local plastic deformation stage, thereby being accurately applied to the finite element simulation process to improve the accuracy of the finite element model, achieving the purpose of accurately predicting the local plastic deformation behavior of the metal material, providing a method for improving the forming capability of the metal material and controlling the forming process, and solving the problem that the hardening behavior of the metal material in the local plastic deformation stage is difficult to predict. The automobile forming process and the aviation process are better guided.
Drawings
FIG. 1 is a flow chart of a weighted constitutive equation method for accurately describing local plastic deformation behavior.
FIG. 2 is an engineering stress-strain curve of Ti-6Al-4V alloy.
FIG. 3 is a graph of uniaxial tensile force versus displacement for a Ti-6Al-4V alloy.
FIG. 4(a) is a linear fit of the elastic deformation phase of a Ti-6Al-4V alloy.
FIG. 4(b) is a fitting procedure of uniform plastic deformation of Ti-6Al-4V alloy.
Fig. 5 shows the fitting process of the initial values of the coefficients of the sub-constitutive equation.
FIG. 6 is a final comparison of uniaxial tensile force versus displacement curves obtained from tests and finite element simulations.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention aims at the problem that the hardening behavior of the metal material is difficult to predict at the local plastic deformation stage, and discloses a weighted constitutive equation description method combined with finite element simulation, the method obtains the weighted constitutive equation by carrying out weighted design on constitutive equations with different characteristics, embeds the weighted constitutive equation into a subprogram of the finite element simulation, thereby establishing a finite element model of the uniaxial tensile deformation of the metal material, carrying out finite element simulation to obtain a force and displacement curve, further comparing the force and displacement curve with the force and displacement curve obtained by the uniaxial tensile test, adjusting the weighting factor and the sub-constitutive equation of the weighted constitutive equation according to the difference between the two curves to make the force and displacement curves of the uniaxial tensile test and the finite element simulation consistent, the finally adjusted weighting constitutive equation is the constitutive equation method capable of accurately describing the local plastic deformation behavior.
Referring to fig. 1, the method of the present invention comprises the following steps:
1. the specific form of the constitutive equation of the weighted design is as follows:
σ＝qK(p+0)n+(1-q)f(p)
wherein q is a weighting factor, K is a strength coefficient, n is a strain hardening index,0in order to be pre-strained,pfor plastic strain, σ is true stress, K: (p+0)nIs the principal constitutive equation of Swift, f: (p) Is a sub-constitutive equation, f: (p) Selecting according to the comparison of the strain intervals of the local plastic deformation stage and the uniform deformation stage of the metal material; during selection, when the strain interval of the local plastic deformation stage is smaller than that of the uniform deformation stage, selecting a Voce equation as a secondary constitutive equation; when the strain interval of the local plastic deformation stage is larger than that of the uniform deformation stageWhen the equation is expressed, a fourth-order polynomial is selected as a second-order constitutive equation;
the Voce constitutive equation is:
σ＝σ0-σ0A exp(-βp)
wherein sigma0For saturation stress, A and beta are the Voce equation material coefficients.
The cubic polynomial constitutive equation is:
in the formula, a, b, c, d and e are coefficients of a fourth-order polynomial.
2. And preparing a uniaxial tensile standard test piece, and performing a uniaxial tensile test so as to obtain an engineering stress-strain curve and a force-displacement curve.
3. When the sub-constitutive equation is Voce constitutive equation, K, n in the weighted constitutive equation,0、σ0The method for obtaining A and beta is as follows:
the engineering stress-strain curve in the uniform deformation stage is converted by the following formula
σ＝s(1+e)
＝ln(1+e)
Wherein s is engineering stress, e is engineering strain, and e is true strain;
the elastic modulus E is obtained by linear fitting of an elastic stage, and then the elastic modulus E is obtained by processing the data through the-/EpFinally, to σ andpdata utilization of (a ═ K: (a:)p+0)nAnd σ ═ σ -0-σ0A exp(-βp) Fitting to obtain K, n,0、σ0A and beta parameter values.
When the second order constitutive equation is a fourth order polynomial, a preliminary curve point of the weighted constitutive equation after necking is preliminarily given according to the necking stage form of the engineering stress-strain curve of the uniaxial tension standard test piece, and the preliminary curve point is expressed by sigma-K (K)p+0)nThe extension curve is taken as a reference to float or descend, and then fitting is carried out to obtain a quadratic polynomial
Is a primary constitutive equation;
4. an initial value of the weighting factor q of a weighting constitutive equation is given.
5. Embedding the preliminarily determined weighted constitutive equation into a subprogram of finite element simulation, thereby establishing a finite element model of uniaxial tensile deformation of the metal material, and obtaining a force and displacement curve through finite element simulation.
6. Comparing the obtained force and displacement curve of the finite element simulation with the force and displacement curve obtained by the uniaxial tensile test, and taking the force and displacement curve obtained by the uniaxial tensile test as a reference, wherein the reference is the sigma-sigma0-σ0A exp(-βp) In the case of a secondary constitutive equation, if a force and displacement curve obtained in a necking stage by finite element simulation is higher than a force and displacement curve obtained in a uniaxial tensile test, the q value is reduced, otherwise, the q value is increased, so that the force and displacement curve obtained by finite element simulation is consistent with the force and displacement curve obtained by the uniaxial tensile test; if the adjustment can not be consistent, the quadratic constitutive equation is changed into a quartic polynomial;
when a fourth-order polynomial is adopted as a second-order constitutive equation, the adjustment process is as follows:
firstly, adjusting a quadratic polynomial quadratic equation curve, fitting to obtain a quadratic polynomial coefficient, and repeatedly iterating the fitting process until a force and displacement curve obtained by finite element simulation is consistent with a force and displacement curve obtained by a uniaxial tensile test;
and a weighting constitutive equation formed by the finally adjusted weighting factor q and the coefficient of the secondary constitutive equation is a final weighting constitutive equation, and the final weighting constitutive equation is utilized to describe the local plastic deformation behavior of the metal material.
Examples
The method for accurately describing the local plastic deformation behavior of the metal material comprises the following steps of:
1) in this example, a standard uniaxial tensile sample of the Ti-6Al-4V alloy was prepared by using the Ti-6Al-4V alloy as a material to be implemented, and a uniaxial tensile test was performed on a tensile tester to obtain a stress-strain curve and a force-displacement curve of the Ti-6Al-4V alloy, as shown in fig. 2 and 3, respectively.
2) As shown in FIG. 4(a), the elastic modulus value of 120.7MPa is obtained by linear fitting of the elastic deformation stage of the stress-strain curve of the Ti-6Al-4V alloy, and the fitted force-displacement curve is shown in FIG. 3.
3) The stress and the strain from the beginning of deformation to the maximum engineering stress (the beginning of local plastic strain) of the selected Ti-6Al-4V alloy are converted into true stress and true strain by the following formula:
σ＝s(1+e)
＝ln(1+e)
then the converted true strain is utilized and the data is processed by the/E to obtainpFinally σ andpdata utilization of (a ═ K: (a:)p+0)nFitting is performed, as shown in FIG. 5, to obtain K, n and0the parameter values were 1207MPa, 0.05638, 0.0039, respectively.
4) As shown in fig. 4(b), according to the curve form of the Ti-6Al-4V alloy at the local plastic deformation stage, if the strain interval at the local plastic deformation stage is larger than that at the uniform deformation stage, a quartic polynomial is selected as a quadratic constitutive equation, and a preliminary curve point of the weighted constitutive equation after necking is preliminarily given, where σ ═ K (b) is used as the preliminary curve pointp+0)nFloating up by taking the epitaxial curve as a reference, and then fitting to obtain a
For the initial values of the sub-constitutive equations, as shown in FIG. 5, the initial values of a, b, c, d, e of the sub-constitutive equations are 1476, 4147, -2475, -1230, 904.
5) Setting the value of the initial weighting factor q to be 0.8, embedding the weighting constitutive equation into a user subprogram VUMAT of ABAQUS software, utilizing ABAQUS software to simulate the uniaxial tension process of Ti-6Al-4V alloy in a finite element manner, obtaining a force and displacement curve of the finite element simulation process and comparing the force and displacement curve obtained by the uniaxial tension test in figure 3, if the force versus displacement curve obtained from the finite element simulation after necking is higher than the force versus displacement curve obtained from the experiment, then the q value is adjusted downwards, the process is carried out, when the difference between the maximum stress of the force and displacement curve obtained by finite element simulation and the maximum stress of the force and displacement curve after necking obtained by uniaxial tensile test is less than 100MPa, the adjustment of the q value is stopped, the coefficient value of the secondary constitutive equation is adjusted, and (3) fine tuning is carried out by giving the epitaxial points of the initial weighted constitutive equation, fitting the coefficient values of the new secondary constitutive equation, and carrying out finite element simulation again to finally enable the finite element simulation to execute the iterative process shown in the figure 1. The q is adjusted mainly to adjust the position of the simulation curve, and the coefficients of the sub-constitutive equation are adjusted mainly to adjust the shape of the simulation curve. When the force and displacement curve obtained by finite element simulation is consistent with the force and displacement curve obtained by uniaxial tensile test, as shown in fig. 6, the weighted constitutive equation formed by iterating the q and a, b, c, d, e values obtained in the last step is the weighted constitutive equation capable of accurately describing the hardening behavior in the local plastic deformation stage, and in this embodiment, the q and a, b, c, d, e values obtained finally are 0.73, -3282, 83, 3638, 1452, 906 respectively. The final weighted constitutive equation is
And describing the local plastic deformation behavior of the metal material by using the final weighted constitutive equation.
Claims (7)
1. A method for accurately describing local plastic deformation behavior of a metal material is characterized by comprising the following steps:
weighting design is carried out on constitutive equations with different characteristics to obtain weighted constitutive equations;
embedding the weighted constitutive equation into a subprogram of finite element simulation, establishing a finite element model of uniaxial tensile deformation of the metal material, and performing finite element simulation to obtain a force and displacement curve;
comparing the force and displacement curve simulated by the finite element with the force and displacement curve obtained by the uniaxial tensile test, and adjusting the weighting factor and the coefficient of the weighted constitutive equation according to the difference between the force and displacement curve simulated by the finite element and the force and displacement curve obtained by the uniaxial tensile test so that the force and displacement curve simulated by the finite element is consistent with the force and displacement curve obtained by the uniaxial tensile test; and describing local plastic deformation behavior of the metal material by using the weighted constitutive equation at the moment.
2. The method for accurately describing the local plastic deformation behavior of the metal material according to claim 1, wherein the weighted constitutive equation is as follows:
σ＝qK(p+0)n+(1-q)f(p)
wherein q is a weighting factor, K is a strength coefficient, n is a strain hardening index,0in order to be pre-strained,pfor plastic strain, σ is true stress, K: (p+0)nIs the principal constitutive equation of Swift, f: (p) Is a sub-constitutive equation, f: (p) Selecting according to the comparison of the strain intervals of the local plastic deformation stage and the uniform deformation stage of the metal material;
during selection, when the strain interval of the local plastic deformation stage is smaller than that of the uniform deformation stage, selecting a Voce equation as a secondary constitutive equation; when the strain interval of the local plastic deformation stage is larger than the polynomial equation of the uniform deformation stage, selecting a fourth-order polynomial as a second-order constitutive equation;
wherein, the Voce constitutive equation is as follows:
σ＝σ0-σ0Aexp(-βp)
in the formula, σ0For saturation stress, A and beta are Voce equation material coefficients;
the cubic polynomial constitutive equation is:
in the formula, a, b, c, d and e are coefficients of a fourth-order polynomial.
3. The method for accurately describing the local plastic deformation behavior of the metal material as claimed in claim 2, wherein the method is characterized in that when the method is used for accurately describing the local plastic deformation behavior of the metal materialWhen the sub constitutive equation is Voce constitutive equation, K, n in the weighted constitutive equation,0、σ0The method for obtaining A and beta is as follows:
according to a uniaxial tensile standard test, obtaining an engineering stress-strain curve and a force-displacement curve, and converting the engineering stress-strain curve in a uniform deformation stage by using the following formula:
σ＝s(1+e)
＝ln(1+e)
wherein s is engineering stress, e is engineering strain, and e is true strain;
the elastic modulus E is obtained by linear fitting of an elastic stage, and then the elastic modulus E is obtained by processing the data through the-/EpFinally, to σ andpdata utilization of (a ═ K: (a:)p+0)nAnd σ ═ σ -0-σ0Aexp(-βp) Fitting to obtain K, n,0、σ0A and beta parameter values.
4. The method for accurately describing the local plastic deformation behavior of the metal material as claimed in claim 2, wherein when the second order constitutive equation is a fourth order polynomial, the initial value of the coefficients of the second order constitutive equation in the weighted constitutive equation is obtained as follows:
according to the necking stage form of the engineering stress-strain curve of the uniaxial tension standard test piece, giving a preliminary curve point of a weighted constitutive equation after necking, wherein the preliminary curve point is represented by sigma K (K)p+0)nAnd the extension curve floats upwards or descends as a reference, then fitting is carried out to obtain a fourth-order polynomial, and the fourth-order polynomial is used as a primary-order constitutive equation.
5. The method of claim 2, wherein the force and displacement curve obtained by the uniaxial tensile test is used as a reference for σ ═ σ ·, when the force and displacement curve of the finite element simulation is compared with the force and displacement curve obtained by the uniaxial tensile test0-σ0Aexp(-βp) In the case of a sub-constitutive equation, the weighting factors are adjustedMaking the force and displacement curve of finite element simulation consistent with the force and displacement curve obtained by uniaxial tensile test, and if the force and displacement curve can not be adjusted to be consistent, converting the quadratic equation into a fourth-order polynomial; and for the condition that the quartic polynomial is used as the quartic constitutive equation, adjusting the weighting factor and the quartic polynomial coefficient of the weighted constitutive equation to enable the force and displacement curve of the finite element simulation to be consistent with the force and displacement curve obtained by the uniaxial tensile test.
6. The method for accurately describing the local plastic deformation behavior of the metal material as claimed in claim 5, wherein when the weighting factors and the coefficients of the weighted constitutive equations are adjusted:
for σ ═ σ0-σ0Aexp(-βp) In the case of a secondary constitutive equation, if a force and displacement curve obtained in a necking stage by finite element simulation is higher than a force and displacement curve obtained in a uniaxial tensile test, the q value is reduced, otherwise, the q value is increased, so that the force and displacement curve obtained by finite element simulation is consistent with the force and displacement curve obtained by the uniaxial tensile test;
when sigma is sigma0-σ0Aexp(-βp) When the force and displacement curve of the finite element simulation necking stage is equivalent to the force and displacement curve obtained by the uniaxial tension test and is not completely overlapped, the quadratic equation is converted into a fourth polynomial; or, when the quadratic equation is a fourth-order polynomial, the adjustment process is as follows:
firstly, adjusting a quadratic polynomial quadratic equation curve, fitting to obtain a quadratic polynomial coefficient, and repeatedly iterating the fitting process until a force and displacement curve obtained by finite element simulation is consistent with a force and displacement curve obtained by a uniaxial tensile test;
and the weighting constitutive equation formed by the finally adjusted weighting factor q and the coefficient of the secondary constitutive equation is the final weighting constitutive equation, and the final weighting constitutive equation is utilized to describe the local plastic deformation behavior of the metal material.
7. The method of claim 1, wherein the finite element simulation software is ABAQUS software, and the subroutine of the finite element simulation software is VUMAT.
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| CN112557194A (en) * | 2020-12-09 | 2021-03-26 | 一汽奔腾轿车有限公司 | Development method of high-precision simulation model of metal material |
| CN113901660A (en) * | 2021-10-11 | 2022-01-07 | 本钢板材股份有限公司 | Novel method for determining constitutive equation coefficient of material VOCE |
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