Method for calculating material property parameters

Abstract

To provide a method for calculating material property parameters for isotropic plastic materials, the method taking into account the stress-increment direction dependence in plastic constitutive equations to calculate three material parameters.SOLUTION: The material parameters Par1, Par2, and Par3 are determined by utilizing only test data in a region where both the maximum principal strain and the minimum principal strain in the sheet plane are positive, obtained in Nakajima-type and Marciniak-type test methods widely used for evaluating the two-dimensional formability of metal sheet materials, and by applying the Storen-Rice theory concerning local necking bifurcation of sheet materials in a two-dimensional plane stress state to the test data, so that the parameters can be applied not only to two-dimensional analysis problems but also more broadly to three-dimensional analysis problems.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to a method for calculating material property parameters, and more particularly to a method for determining material parameters of the Goya-Ito plastic constitutive equation that incorporates the directional dependency of stress increments. [Background technology]

[0002] In recent years, numerical simulations using the finite element method (FEM) have been frequently used in sheet metal forming, such as in the formation of automobile bodies, and efforts are being made to minimize the number of processes that require huge costs, such as the basic design of the molds used for forming, and mold modifications, etc. In this context, understanding the stress-strain relationship related to plastic deformation, which evaluates the properties of materials, or the so-called plastic constitutive equation, is important from the perspective of understanding the forming limits of metal components.

[0003] Goya and Ito assumed that the magnitude and direction of the plastic strain increment are functions of the deflection angle α of the stress increment from the current stress direction, and by introducing the parameters μ(α) and β(α) related to these, they introduced a new plastic constitutive equation that relaxes the normality constraint of the plastic strain increment in potential theory. This is a more general expression that can introduce the stress increment direction dependency into the constitutive equation regardless of the existence of a cusp (corner point) on the yield surface where the current stress point is located. The inverse expression of Goya and Ito's stress increment direction dependency law is given by the following equation from Non-Patent Document 1 (see below).

[0004]

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[0005] For the sake of convenience in the description of the present specification, the correspondence between the special notation for each of the tensor quantities in the following formulas, including the above formulas (1) to (4), and the notation used in the following text of the present specification is as shown in Table 1 below (the same applies hereinafter). [Table 1]

[0006] In Equations (1) to (4), dSdev is the deviatoric stress increment tensor, dEdev is the deviatoric strain increment tensor, Sdev is the deviatoric stress tensor, Sbar is the equivalent stress, K is the bulk modulus, dp is the hydrostatic pressure component of the stress increment tensor dS, dEvol is the volumetric strain increment, G is the transverse elastic modulus, H' is the tangent gradient, and μ = μ(α) is the magnitude of the plastic strain increment dEp. Also, α (0≦α≦αmax) is the deflection angle of the deviatoric stress increment tensor dSdev from the unit tensor n in the normal direction of the plastic potential, and β (0≦β≦βmax) is the deflection angle of the plastic strain increment tensor dEp from the unit tensor n in the normal direction of the plastic potential. These are monotonically decreasing transition functions of α (see Figure 1).

[0007] Furthermore, based on numerical analysis of a polycrystalline finite element model, Non-Patent Document 4 (see below) proposes the relationships between μ(α) and β(α) as shown in Equations (5) to (9) below (see FIG. 2).

[0008]

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[0009] Here, Kcmin in equation (8) above represents the minimum value of the coefficient Kc (0≦Kc≦1) in the constant coefficient law proposed in Non-Patent Document 2 (see below) for a fixed stress tensor direction. This value is a non-material parameter that varies depending on the stress tensor direction and is a coefficient for introducing the linear comparison body constitutive law introduced by Hill for bifurcation analysis of plastic materials. It is known that a large Kc value results in an insufficient bifurcation limit value. Therefore, to obtain more practical results through bifurcation analysis such as forming limit problems, it is necessary to select a Kc value that exhibits the smallest stress increment directional dependency among the linear comparison body constitutive laws for a certain stress direction. This value is denoted as Kcmin (see Non-Patent Documents 2 and 4).

[0010] ΘL is called the Lode angle, and represents the angle from the center of the side of the Tresca-type yield function on the deviatoric stress surface as shown in Figure 2, with its maximum value being ΘS (=π / 6). As with Table 1, for the convenience of this specification, the dimensionless angle of the Lode angle defined by the above equation (9) is shown in Table 2, with the correspondence between the special notation in the equation and the notation in the rest of this specification. [Table 2]

[0011] In the case of an isotropically hardening material, the dimensionless Lode angle TLbar satisfies the equation (11) below as a function of the strain ratio ξ.

[0012]

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[0013] In Non-Patent Document 4, Φ in the above equation (7) is defined as a function of the deflection angle from the uniaxial load direction in the Ilyushin stress space. However, in the present invention, in order to provide extensibility so that it can be easily applied to three-dimensional analysis, the Lode angle ΘL, which is the angle from the center of the edge of the Tresca-type yield function on the deviatoric stress surface, is introduced as shown in the above equation (9) (see Figure 2).

[0014] The material parameters are Par1, Par2, and Par3, and Par1 in particular indicates a single value for uniaxial loading. In order for a series of plastic constitutive equations to be useful in practice, a test method must be established to determine the material parameters included in the proposed functional forms.

[0015] [· Theories on local constriction] (See, for example, Non-Patent Documents 3 and 4 below) It is well known that the Hill criterion for the bifurcation problem of local necking of a rigid-plastic plate shown in Figure 3 does not provide a limiting value in the region where the maximum and minimum principal strain ratios are positive. Subsequent research has revealed that the reason for this is the use of the normal law, i.e., the potential law, for the plastic strain increment.

[0016] However, the incremental form of Hencky deformation theory, which has been considered irrational due to its unclear unloading criteria, differs from plastic potential theory in that a one-to-one relationship exists between stress increments and plastic strain increments, i.e., it has a so-called stress increment direction dependency. Storen and Rice (hereinafter referred to as SR theory) applied this incremental form of Hencky deformation theory to this problem and obtained results that show certain limit values ​​even in the region where Hill's criterion cannot be evaluated. Under these circumstances, various plastic constitutive equations that incorporate the stress increment direction dependency, a characteristic of the incremental form of Hencky deformation theory, have been studied.

[0017] Non-patent document 4 shows that when the constant coefficient law is introduced into SR theory, the bifurcation condition for isotropic materials that follow Swift's n-th power law can be derived as follows:

[0018]

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[0019] The strain ratio ξ is defined by the above equation (12), and n is the relationship between the Mises equivalent stress Sbar and the equivalent plastic strain Epbar for isotropically hardening materials, as expressed by Swift's n-th power law, which is shown in the equation (17) below.

[0020]

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[0021] is the n value in

[0022] λ indicates the direction of the necking band in Hill's local necking problem shown in Figure 3, and is defined as equations (18) and (19) below.

[0023]

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[0024] The bifurcation analysis using the above equation (13) is as follows.

[0025] 1) First, in the above equation (13), a certain strain ratio ξ and Kc value are given as the load conditions. 2) Next, set Ψ=0 (λ=0), regard the above equation (13) as a quadratic equation with respect to (ε11 / n), and find the value of (ε11 / n). 3) Further increase the Ψ value by a fixed increment ΔΨ within the range of 0≦Ψ≦π / 2 (0≦λ≦∞), and define this as Ψi (=ΔΨ×i, where i ranges from 1 to the maximum step number of the increment), and calculate the limit strain value (ε11 / n)i for each Ψi using the same procedure as in (2) above. 4) Each (ε11 / n)i obtained in the range of 0≦Ψ≦π / 2 by 2) and 3) The minimum value found among these is the in-plane maximum principal strain value that generates local necking for the strain ratio ξ and Kc value, which are the loading conditions specified in 1) above, and the corresponding Ψ indicates the direction in which the necking band occurs.

[0026] An example of the results is shown in FIG. 4 (see Non-Patent Document 3).

[0027] The limit diagram shown in Figure 5, also known as the Forming Limit Diagram or Forming Limit Curve, is obtained by the Marciniak test method or the Nakajima test method. It is understood as a diagram for evaluating the forming limits of thin plates and has been widely adopted in manufacturing sites.

[0028] Currently, the standard forming performance evaluation test method is ISO International Standard No. ISO 12004-2:2021, with the ISO International Standard name "Metallic materials - Determination of forming-limit curves for sheet and strip - Part 2: Determination of forming-limit curves in the laboratory" (Japanese translation: "Metallic materials - Determination of forming-limit curves for sheet and strip - Part 2: Determination of forming-limit curves in the laboratory"), which was issued on 2021-02-10. [Prior art documents] [Patent documents]

[0029] [Non-Patent Document 1] Moriaki Goya and Koichi Ito, "An Expression of the Constitutive Equation of Elastic-Plastic Materials Considering the Dependence of Stress Increment Direction (1st Report, Initially Isotropic Materials with Mises-Type Plastic Potential)" in the Transactions of the Japan Society of Mechanical Engineers (Series A) (Periodic Publication), Vol. 54, No. 504 (1988-8), pp. 1617-1622, 1988. [Non-patent document 2] Koichi Ito, Moriaki Goya, and Kiyoshi Otsu, "An Expression of the Constitutive Equation of an Elastic-Plastic Body Considering the Dependence of Stress Increment Direction (2nd Report, Analysis of Linear Comparator and Elastic-Plastic Circular Tube Buckling)" in Transactions of the Japan Society of Mechanical Engineers (Series A) (Periodic Publication), Vol. 55, No. 520 (1989-12), pp. 2475-2480, 1989. [Non-patent document 3] Moriaki Goya and Koichi Ito, "An Expression of the Constitutive Equation of Elastic-Plastic Materials Considering the Dependence of Stress Increment Direction (3rd Report, Analysis of Localized Necking of Rigid-Plastic Thin Plates)" in the Transactions of the Japan Society of Mechanical Engineers (Series A) (Periodic Publication), Vol. 56, No. 521 (1990-1), pp. 101-106, 1990. [Non-patent document 4] Moriaki Goya, Koichi Ito, Hiroshi Takahashi, Kiyohiro Miyagi, ELSEVIER, 1995, Journal of Materials Processing Technology (periodical), Vol. 50 (1995), pp. 216-225, "Determination of constitutive parameters by forming-limit tests" DISCLOSURE OF THE INVENTION [Problem to be solved by the invention]

[0030] The experimental procedure for accurately determining the material parameters Par1, Par2, and Par3 in the plastic constitutive equation of Goya-Ito, which takes into account the direction dependency of the stress increment, has not yet been clarified in a form that is useful for practical use.

[0031] The present invention has been made in consideration of the above-mentioned circumstances, and its purpose is to provide a method for calculating material property parameters that can calculate three material parameters of a plastic constitutive equation that takes into account the stress increment direction dependency for isotropic plastic materials. [Means for solving the problem]

[0032] The above-mentioned object of the present invention can be achieved by the following configuration.

[0033] The method for calculating material property parameters of the present invention includes: A method for calculating material parameters through a forming limit diagram of a metal member based on the following formulas (101) to (109), The correspondence between the special notations for the tensor quantities shown in the equations (101) to (120) and the notations used in the text is shown in Tables 3 and 4. In order to calculate the first material parameter Par1 shown in the formula (106) below, the second material parameter Par2 shown in the formula (107) below, and the third material parameter Par3 shown in the formula (107) below, A testing step of preparing M (M≧3) plate-shaped metal test pieces obtained from the metal member and performing a test in which loads are applied to each of the metal test pieces in directions with a plurality of different strain ratios based on a forming limit test method; For each i (i = 1, , M)-th plate-shaped metal test piece obtained based on the test results of the test step, ξi is calculated as (ε22 / n) and (ε11 / n) according to the formula (112) described below. a first calculation step A in which the ratio of Kci is calculated and the corresponding Kci is calculated according to the formula (113) to the formula (116) described later, or a first calculation step B in which the corresponding Kci is calculated according to the formula (120) described later. a second calculation step of evaluating the individual errors Ei and the total error TE based on the calculation results in the first calculation step A or calculation step B and equations (118) and (119) described below; and a third calculation step of calculating values ​​of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 based on each of the errors Ei evaluated in the second calculation step and the total error TE.

[0034] [Table 3] [Table 4]

[0035]

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[0036]

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[0037]

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[0038] This invention relates to a method for calculating material property parameters, and in particular proposes a method for calculating and determining three material parameters Par1, Par2, and Par3 of the plastic constitutive equation that takes into account the stress increment direction dependency developed by Kureya and Ito in the above-mentioned Non-Patent Documents 1 and 4 for isotropic plastic materials.

[0039] Until now, the Mises-type yield function has been used as the plastic potential, and the normal law has been applied to the plastic strain increment. However, the existence of corner points on the yield surface due to the existence of slip systems in single crystals, as typified by the corner points of the Tresca-type yield function, has been suggested, and the dependence of the strain increment on the direction of the stress increment has been discussed experimentally and theoretically.

[0040] According to the method for calculating material property parameters of the present invention, the three material parameters Par1, Par2, and Par3 of the Goya-Ito stress increment direction dependent plastic constitutive equation can be calculated (determined) for real materials, thereby resolving the issue between the Mises-type and Tresca-type yield functions that existed for isotropic materials.

[0041] In this way, by applying the Goya-Ito stress increment direction-dependent plastic constitutive equation to FEM analysis, which has recently become widely used as an indispensable tool in the field of plastic processing manufacturing of metal materials, and conducting detailed analysis, it is possible to analyze the forming limits of metal components, including sheet metal forming.

[0042] In particular, in FEM analysis where the thin plate forming process or forming limits are issues, the three material parameters Par1, Par2, and Par3 are calculated through forming limit tests of the same material, which makes it possible to obtain more reliable analysis results.

[0043] We propose the Lode angle, instead of Ilyushin's five-dimensional deviatoric stress plane, as a parameter to express the direction of the current deviatoric stress. This allows us to easily determine the direction of the current stress on the Tresca-type yield function on the deviatoric principal stress plane, and we can easily develop the Goya-Ito stress increment direction-dependent plastic constitutive equation so that it can be easily applied to three-dimensional analysis.

[0044] Even for non-thin sheet materials, such as block-shaped metal ingots, material parameters can be determined by cutting them into thin sheets and conducting Marciniak or Nakajima forming limit tests.

[0045] The present invention has been briefly described above. The details of the present invention will be further clarified by reading the following description of the preferred embodiments (hereinafter referred to as "embodiments") or specific examples (hereinafter referred to as "examples") with reference to the accompanying drawings. [Brief explanation of the drawings]

[0046] [Figure 1] This figure explains the concept of the deflection angle α of the stress increment dS from the plastic potential normal tensor n in the deviatoric stress space and the deflection angle β(α) of the plastic strain increment tensor dEp in the stress increment direction-dependent plastic constitutive equation proposed by Goya and Ito. [Figure 2] This is a diagram explaining the Mises-type yield surface, Tresca-type yield surface, and Lode angle on the deviatoric principal stress π-plane. [Figure 3] FIG. 1 is a diagram illustrating typical parameters in Hill's local necking problem. [Figure 4] This figure explains the forming limit diagram obtained by applying the Ito-Goya constant coefficient law to the Storen-Rice theory. [Figure 5] 1 is a graph showing the meaning of experimental points obtained by Marciniak-type or Nakajima-type forming limit tests, which are conventional techniques, and a forming limit diagram. [Figure 6]FIG. 1 is a diagram illustrating a limit diagram using material parameters obtained in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0047] Hereinafter, one or more embodiments or one or more examples that specifically disclose a method for calculating material property parameters according to the present invention will be described in detail with appropriate reference to the accompanying drawings.

[0048] However, more detailed explanations than necessary may be omitted, for example, detailed explanations of well-known matters or redundant explanations of substantially identical configurations may be omitted, in order to avoid unnecessary redundancy in the following explanation and to facilitate understanding by those skilled in the art.

[0049] The accompanying drawings and the following description are provided to enable those skilled in the art to fully understand the present disclosure, and are not intended to limit the subject matter described in the claims. Each of the accompanying drawings should be referenced according to the orientation of the reference numerals.

[0050] Also, unless otherwise indicated, all numbers expressing parameters, reaction conditions, concentrations of ingredients, and so forth used in this specification and the appended claims are to be understood as being modified in all instances by the term "about." Accordingly, unless indicated to the contrary, the numerical parameters set forth in the following specification and appended claims are approximations that may vary depending, at least in part, on particular analytical techniques.

[0051] <Terminology> The terms "comprising" or "characterized by," which are synonymous with "comprising" and "containing," are to be construed in an inclusive or open-ended sense and do not exclude additional, unrecited elements or method steps. "Comprising" is a term of art used in claim language that means that the named claim element is required, but that other claim elements may be added to further form structure within the scope of the claim.

[0052] Also, as used herein, the phrase "consisting of" excludes any element, step, or ingredient not specified in the claim. When the phrase "consisting of (or variations thereof)" appears in a section of the body of a claim rather than immediately following the preamble, it limits only the elements set forth in that section and does not exclude other elements from the claim as a whole. As used herein, the phrase "consisting essentially of" limits the scope of a claim to those elements or method steps specified in addition to those that do not materially affect the main and novel feature(s) of the claimed subject matter.

[0053] With respect to the terms "comprising," "consisting of," and "consisting essentially of," when one of these three terms is used herein, the presently disclosed and claimed subject matter may also include the use of either of the other two terms. Thus, in some embodiments not expressly recited otherwise, any instance of "comprising" may be replaced by "consisting of" or "consisting essentially of."

[0054] The term "process" or "step" may be used explicitly or implicitly in connection with process or method features, but no order or sequence is limited among such explicit processes or steps or among implicit processes or steps unless the order or sequence is stated.

[0055] First Embodiment In this embodiment, the steps for solving the problem of the present invention will be roughly divided into three stages: a first calculation step A or a first calculation step B, a second calculation step, and a third calculation step. In the first step, the first calculation step A or the first calculation step B described below is executed. In the second step, which is the step following the first step, the second calculation step described below is executed. In the second step, which is the step following the second step, the third calculation step is executed. In addition, when explaining the first calculation step A or the first calculation step B, the common parts will be explained first, and then the other parts of the first calculation step A or the first calculation step B will be explained individually below.

[0056] [· Portion common to first calculation step A and first calculation step B] In the aforementioned Non-Patent Document 4, the constant coefficient law is introduced into the SR theory, and as a result, the local necking bifurcation conditions for the Swift's n-th power law isotropically hardening material shown in the above equation (17) are given as shown in the above equations (13) to (16).

[0057] In many forming limit diagrams, it has been observed that in the region where both the in-plane maximum principal strain and the in-plane minimum principal strain are positive (ξ≧0), the direction of local necking bands is almost perpendicular to the in-plane maximum principal strain direction, i.e., the x1-axis direction shown in Figure 3. This has also been shown theoretically to be Ψ=0 (λ=0).

[0058] The present invention utilizes this fact and is obtained by substituting λ=0 in the above equation (13).

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[0059] Utilize the following.

[0060] Here, suppose that seven data points as shown in Table 5 below are obtained from tests in several different load directions using the Marciniak or Nakajima forming limit test on a thin plate material (an example of a "metallic component") (an example of a "test step"). The thin plate material in this embodiment is a thin metal plate or a thin plate cut out from a metal block member.

[0061] [Table 5]

[0062] Theoretically, the number of data points M can be M ≥ 3 because there are three unknown material parameters. However, to obtain accurate values, it is better to obtain a large amount of data for widely differing ξi values. Table 5 shows the case where M = 7. The resulting data from Table 5 is plotted in Figure 6 in the first quadrant of the in-plane maximum principal strain (ε11 / n) and in-plane minimum principal strain (ε22 / n) coordinate system normalized by the exponent n value of Swift's n-th power law.

[0063] The Lode angle ΘL can be treated as a plane stress when the load is only within the plane of the thin plate material, and the following equation holds for the dimensionless angle TLbar (see Table 4 above) for isotropically hardened materials.

[0064]

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[0065] Furthermore, in the case of isotropically hardening materials, the following equation (23) holds true, so

[0066]

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[0067] Ultimately, the above equation (22) can be expressed as the above equation (11) using the strain ratio ξ.

[0068]

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[0069] In Table 5, the strain ratio ξi and (ε11 / n)i corresponding to each plot of the test data are given as the load direction and limit strain value of the test. Table 5 shows the case where the total number of data is M=7.

[0070] The above has described the common parts of the following first calculation step A and first calculation step B. Next, the first calculation step A and first calculation step B will be described individually.

[0071] [First calculation step A] The procedure for obtaining a numerical solution from equation (28) described below as the first calculation step A is as follows.

[0072] As mentioned above, by substituting ξi and (ε11 / n)i into equation (28) below and solving it as a quadratic equation for Kc, Kci corresponding to each i-th plot can be found. However, the formula for solving the original quadratic equation contains a compound sign, as shown below.

[0073]

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[0074] However, since the Kc value can only take positive values, the compound sign in the above equation (24) should only take negative signs, as shown in the following equation, resulting in equation (28) below.

[0075]

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[0076] Here, Ai, Bi, and Ci are defined in the above equations (25) to (27).

[0077] By applying the above equation (28) to the M data for each plot, M different Kci values ​​can be determined. The Kci values ​​corresponding to the test data in Table 5 are shown in Table 6 below.

[0078] [First calculation step B] The procedure for obtaining a numerical solution from equation (29) below, which is the analytical solution in the first calculation step B, is as follows.

[0079] ξi and (ε11 / n)i in Table 5 mentioned above By substituting this into equation (29) below, the Kci value corresponding to each i-th plot can be obtained.

[0080]

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[0081] By applying the above equation (29) to the M data for each plot, M different Kci values ​​can be determined. The Kci values ​​corresponding to the test data in Table 5 are shown in Table 6 below.

[0082] [Table 6]

[0083] Table 6 shows the Kci values ​​obtained by the first calculation step A and the first calculation step B, and as a matter of course, the results obtained by either the first calculation step A or the first calculation step B are the same.

[0084] The above has described the first calculation step A and the first calculation step B. Next, the subsequent steps, the second calculation step and the third calculation step, will be described.

[0085] [Second calculation step] In the above equation (11), the dimensionless Lode angle (TLbar) is given as a function of ξ, and the (TLbar)i value corresponding to each ξi in Table 5 can be found.

[0086] Using the formula (30) below, which is the result of substituting the (TLbar)i value into the formulas (7) and (8),

[0087]

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[0088] The material parameters Par1, Par2, and Par3 can be determined by the least squares method as follows:

[0089] First, the Kc value for the same ξi in Table 6 is taken as Kci, and the difference between this and Kcmin{(TLbar)i} obtained from the above equation (30) is denoted as Ei and defined in the equation (31) below.

[0090]

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[0091] The Kc value can be in a wide range of 0≦Kc≦1, and in the above equation (31), the square of each difference is (Kci) 2 By dividing by and normalizing, it is possible to take into consideration the case where the Kc value is a very small value and to evaluate the error evaluation in each plot with the same weight. That is, in this embodiment, in defining the error, the value obtained by dividing by the square of the Kci value is defined as the error, rather than the squared error due to the difference between the Kci value and Kcmin{(TLbar)i}. This makes it possible to normalize the influence of the magnitude of the Kci value itself on the total error TE to the same extent.

[0092] Furthermore, the total error TE is defined as the sum of the squared errors calculated for each plot by the above equation (31) using the following equation, as shown in equation (32) below.

[0093]

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[0094] [Third calculation step] The object of the present invention is achieved by finding a combination of material property parameters Par1, Par2, and Par3 that minimizes the total error TE defined by the above equation (32).

[0095] In this case, for the search candidates for the first material parameter Par1, values ​​at 40 or more division points in the range of 0 to 0.5 are selected as a first group of value candidates. For the search candidates for the second material parameter Par2, values ​​at 100 or more division points in the range of 0 to 0.5 are selected as a second group of value candidates. For the search candidates for the third material parameter Par3, values ​​at 40 or more division points in the range of 0 to 3 are selected as a third group of value candidates.

[0096] From the first value candidate group, the second value candidate group, and the third value candidate group selected in this manner, the combination of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 that minimizes the value of the total error TE in the above equation (32) is searched for, and the material property parameters Par1, Par2, and Par3 are calculated.

[0097] As a specific search method, the Newton-Raphson method may be used. That is, in this embodiment, the search ranges are set as follows: for the first material parameter Par1, the range is 0 to 0.5; for the second material parameter Par2, the range is 0 to 0.5; and for the third material parameter Par3, the range is 0 to 3. Then, using the Newton-Raphson method, a combination of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 that minimizes the value of the aforementioned total error TE is searched for and determined within the set ranges.

[0098] Furthermore, although a linear constitutive equation with a coefficient Kc (0≦Kc≦1) introduced by Ito et al. (see Non-Patent Document 2 mentioned above) for isotropic plastic materials is used as a linear comparison rule, this is not interpreted as a material parameter in the present invention, which is essentially different from past patent documents (for example, Japanese Patent Laid-Open No. 2007-285832 (Nippon Steel Corporation) and Japanese Patent Laid-Open No. 2009-68919 (Sumitomo Metal Industries, Ltd.)), in which Kc is positioned as a material parameter.

[0099] The material parameters Par1, Par2, and Par3 included in the transition function β(α), which represents the swing angle of the plastic strain increment, are applied to the Storen-Rice local necking theory using the coefficient Kc of the linear comparison law, and the calculated limit values ​​in each load direction are calculated through the ability to match the experimental forming limit data as closely as possible in the least squares sense.

[0100] The material parameters Par1, Par2, and Par3 determined through the process according to the present invention for these seven data points are calculated (determined) as follows: Note that the equation (33) below shows an example of the material parameter value according to this embodiment, and various material parameters Par1, Par2, and Par3 are determined according to the procedure described above in accordance with the numerical values ​​obtained from the test results described above.

[0101]

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[0102] As shown in Figure 6, the values ​​of Equation (33) obtained by the error minimization procedure were substituted into Equations (7) and (8), and the forming limit results obtained by the conventional bifurcation analysis based on Equation (21) were shown by the solid line in the figure. It can be seen that the solid line clearly shows the trend of the experimental points in the entire region. This demonstrates the usefulness and practicality of the present invention.

[0103] The present disclosure has been described above with reference to the accompanying drawings, with reference to one or more specific embodiments or examples thereof as preferred examples, but the present invention is not limited to these embodiments or examples. It is clear that a person skilled in the art can conceive of various modifications or alterations within the scope of the claims, and these modifications also naturally fall within the technical scope of the present disclosure.

[0104] For example, the parameter determination method for the stress increment direction-dependent plastic constitutive equation using the forming limit test described above is not limited to isotropic materials. The present invention can be expanded to certain anisotropic materials as well. For example, in the case of sheet metal forming, the material is often treated as an in-plane isotropic material in practice by adopting the Lankford r-value, which averages the in-plane anisotropy. In such cases, the method of the present invention is useful.

Claims

1. A method for calculating material parameters through a forming limit diagram of a metal member based on the following formulas (1) to (9), The correspondence between the special notations for the tensor quantities shown in the following formulas (1) to (20) and the notations described in the claims is shown in Tables 1 and 2 below. In order to calculate the first material parameter Par1 shown in the following formula (6), the second material parameter Par2 shown in the following formula (7), and the third material parameter Par3 shown in the following formula (7), a testing step of preparing M (M≧3) plate-shaped metal test pieces obtained from the metal member, and performing a test in which loads are applied to each of the metal test pieces in directions with a plurality of different strain ratios based on a forming limit test method; a first calculation step A in which ξi is calculated as a ratio between (ε22 / n) and (ε11 / n) according to the formula (12) described later for each of the i (i = 1, ..., M)-th plate-shaped metal test pieces obtained based on the test results of the test step, and each corresponding Kci is calculated according to the formulas (13) to (16) described later; a second calculation step of evaluating the individual errors Ei and the total error TE based on the calculation results of the first calculation step A and the equations (18) and (19) described below; a third calculation step of calculating values ​​of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 based on each of the errors Ei evaluated in the second calculation step and the total error TE. Method for calculating material property parameters. 【number】 【number】 [Equation 1] [Equation 2] [Equation 3]

2. In the second calculation step, Based on the above-mentioned formulas (13) to (16), each of the errors Ei is derived by the formula (18) described later, and the total error TE is calculated based on the formula (19) described later; In the third calculation step, determining the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3, respectively, by searching for a combination of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 that minimizes the calculated total error TE; The method for calculating material property parameters according to claim 1 . [Equation 4]

3. Selecting values ​​of 40 or more division points in the range of 0 to 0.5 as search candidates for the first material parameter Par1 as a first value candidate group; Selecting values ​​of 100 or more division points in the range of 0 to 0.5 as search candidates for the second material parameter Par2 as a second value candidate group; Regarding search candidates for the third material parameter Par3, values ​​of 40 or more division points in the range of 0 to 3 are selected as a third value candidate group; a combination of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 that minimizes the value of the total error TE in the formula (19) is searched for from among the first value candidate group, the second value candidate group, and the third value candidate group; The method for calculating material property parameters according to claim 2.

4. A combination of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 is searched for using the Newton-Raphson method, in which the value of the total error TE in the formula (19) is minimized, in a range of 0 to 0.5 for the search candidate of the first material parameter Par1, in a range of 0 to 0.5 for the search candidate of the second material parameter Par2, and in a range of 0 to 3 for the search candidate of the third material parameter Par3. The method for calculating material property parameters according to claim 2.

5. In the definition of the error in the above equation (18), the error is defined as the value obtained by dividing the Kci value by the square of the Kci value, rather than the square error due to the difference between the Kci value and Kcmin{(TLbar)i}. The method for calculating material property parameters according to claim 2.

6. A method for calculating material parameters through a forming limit diagram of a metal member based on the following formulas (1) to (9), The correspondence between the symbols of the special notations for the tensor quantities shown in the following formulas (1) to (20) and the notations described in the claims is shown in Tables 3 and 4 below. In order to calculate the first material parameter Par1 shown in the following formula (6), the second material parameter Par2 shown in the following formula (7), and the third material parameter Par3 shown in the following formula (7), a testing step of preparing M (M≧3) plate-shaped metal test pieces obtained from the metal member, and performing a test in which loads are applied to each of the metal test pieces in directions with a plurality of different strain ratios based on a forming limit test method; a first calculation step B in which ξi is calculated as a ratio of (ε22 / n) to (ε11 / n) according to the formula (12) described later for each of the i (i = 1, ..., M)-th plate-shaped metal test pieces obtained based on the test results of the test step, and each corresponding Kci is calculated according to the formula (20) described later, which is an analytical solution; a second calculation step of evaluating the individual errors Ei and the total error TE based on the calculation results in the first calculation step B and the equations (18) and (19) described below; a third calculation step of calculating values ​​of the first material parameter Par1, the second material parameter Par2, and the third material parameter Par3 based on each of the errors Ei evaluated in the second calculation step and the total error TE. Method for calculating material property parameters. 【number】 【number】 [Equation 4] [Equation 6] [Equation 7] [Equation 8]

7. The metal member is a thin metal plate or a thin metal plate cut out from a metal block member. The method for calculating material property parameters according to claim 1 or 6.

8. The forming limit test in the test step is a Marciniak or Nakajima forming limit test, The method for calculating material property parameters according to claim 1 or 6.

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