JP4621216B2 - Fracture limit acquisition method and apparatus, program, and recording medium - Google Patents

Description

  The present invention relates to a method and apparatus for acquiring a fracture limit of a thin plate made of a metal material, a program, and a recording medium, and is particularly suitable as a criterion for judging fracture of a material fracture in a collision process of an automobile member subjected to press molding.

The margin for fracture is generally determined using a plate thickness reduction rate or a forming limit diagram (FLD). FLD is a diagram showing a maximum principal strain that gives a fracture limit for each minimum principal strain, and can also be used in a collision analysis. The experimental FLD measurement method generally involves drawing a circle or lattice pattern on the surface of a metal plate in advance by etching, etc., and then breaking it by hydroforming or overhanging with a rigid tool. The fracture limit strain is measured from the amount. The fracture limit line is obtained by proportionally loading a metal plate for various in-plane strain ratios, plotting the fracture limit strain at each strain ratio on the main strain axis, and connecting them with a line.

などがあり、Keelerの経験則で板厚の影響を補正することで得られる。従来の破断評価方法は、これら破断限界線と塑性変形過程の有限要素法によるシミュレーションの結果から得られる各部位の歪み状態との位置関係を比較することで評価し、変形過程の歪みがこの限界歪みに達したときに破断、もしくは、その危険性が高いと判断する。 FIG. 1 shows the fracture limit line measured by experiment.
As FLD prediction methods, a combination of Hill's local constriction model and Swift's diffusion constriction model, Marciniak-Kuczynski method,

It can be obtained by correcting the influence of plate thickness according to Keeler's rule of thumb. The conventional fracture evaluation method evaluates by comparing the positional relationship between these fracture limit lines and the strain state of each part obtained from the simulation results of the plastic deformation process by the finite element method. When strain is reached, it is judged that the fracture or the risk is high.

1993, Hosford, Metal Forming, 319 2004, Plasticity and processing 45, 123 2004, CAMP-ISIJ 17, 1063 1988, theory A, 57, 1617

  As shown by the breaking limit line in FIG. 2, it is known that the breaking limit line changes greatly depending on the strain path. For example, (a) compared to the fracture limit line when loaded with a linear path change with no deformation path change, (b) the fracture limit line in the case of a path change that applies equal biaxial tensile deformation after uniaxial tension pre-strain. (C) In the case of (c) the change in the path to apply uniaxial tension after biaxial tensile pre-strain, or (d) the change in the path to apply the plane strain tensile deformation after pre-strain of biaxial tension, etc., the fracture limit line decreases. This is clear from many experiments and numerical analysis.

  In the impact deformation process of car body parts that have undergone press deformation or pre-deformation in press molding, the deformation path often changes greatly, and when evaluating fracture using the fracture limit line obtained from experiments, depending on the deformation path I have to prepare myriad limit lines. Therefore, in practical use, the fracture evaluation uses a fracture limit line with respect to the proportional load path, and high prediction accuracy cannot be expected.

  It is known that the fracture prediction of the stretch flange portion cannot be predicted with good accuracy even if FLD is used as a fracture criterion. Stretch flange rupture occurs when the elongation strain in the circumferential direction of the material edge reaches a limit value specific to the material. The stress state of the material edge is close to uniaxial tension, but there is a steep stress and strain gradient inward from the material edge, so the fracture limit is the fracture limit strain or stress obtained in the uniaxial tensile test. Compared with a significantly different value. That is, in the case of stretch flange fracture, even if the material end reaches the plastic instability condition and local constriction (thickness constriction) occurs, the inner material excluding the material end does not yet satisfy the plastic instability condition. Restrained by the inner material, the plastic instability condition cannot be obtained as a whole, and the progress of the plate thickness constriction is delayed. Furthermore, in the stretch flange breakage, a large number of plate thickness constrictions occur in the circumferential direction of the material end portion, so that the breakage is delayed. For example, if a plate thickness constriction occurs in one part of the material end, the circumferential stress in the vicinity of the plate thickness constriction is relaxed. However, as the distance from the plate thickness constriction increases, the effect of this stress relaxation decreases, and when the deformation proceeds further, the next plate thickness constriction occurs away from the original plate thickness constriction. As deformation further develops, new necking occurs. By repeating this process, a large number of sheet thickness constrictions occur in the circumferential direction of the material edge, and the sheet thickness constrictions grow. Here, the plate thickness constriction generated before that does not grow and break, because it is constrained by a material with less strain and does not satisfy the plastic instability in the entire circumferential direction of the material end. Therefore, in the stretch flange break, even if a plate thickness constriction occurs at one place in the circumferential direction of the material end, it is delayed without leading to the break.

  Thus, the method for predicting the stretch flange breakage is not easy due to the existence of a strain gradient inward from the end of the material and the delay effect that does not break even if one circumferential direction fills the local constriction. Not.

  The present invention aims to solve the above-mentioned problems of the prior art, and when determining the breaking limit of a thin plate in a process including one or more deformation path changes, the breaking limit line is easily and efficiently obtained. Another object of the present invention is to provide a fracture limit acquisition method and apparatus, a program, and a recording medium that can determine a fracture limit with high prediction accuracy.

  As a result of earnest research to solve the above problems, the present inventor has conceived various aspects of the invention described below.

  The fracture limit acquisition method of the present invention is a method for acquiring a fracture limit line used for determining a fracture limit of a thin plate made of a metal material, and the fracture limit of the thin plate in a process including one or more deformation path changes. Is determined, the fracture limit line of the strain space obtained by the proportional load path is converted into the fracture limit line of the stress space.

  The break limit line described on the stress space can be represented by a single limit line regardless of the path change. Therefore, by using this as a criterion for determining fracture, the fracture limit of the thin plate in the plastic deformation process including one or more deformation path changes can be determined with high accuracy.

  The fracture limit acquisition device of the present invention is a fracture limit acquisition device for determining a fracture limit of a thin plate in a process including one or more deformation path changes for a thin plate made of a metal material, and obtained by a proportional load path Conversion means for converting the fracture limit line of the strain space into the fracture limit line of the stress space is included.

  The program according to the present invention determines a fracture limit line of a strain space obtained by a proportional load path when determining a fracture limit of the thin sheet in a process including one or more deformation path changes for a thin plate made of a metal material. It is for making a computer perform the procedure converted into a fracture limit line.

  Furthermore, as a result of intensive studies to solve the above-described problems, the present inventors have conceived various aspects of the invention described below. The fracture limit obtaining method of the present invention is a method for obtaining a fracture limit used for determining a fracture limit of a thin plate made of a metal material, and determining the fracture limit of the thin plate in a process including one or more deformation path changes. In the determination, the elongation strain rate λ obtained from the hole expansion test is converted into a fracture limit line of the stress space.

  Since the fracture limit line written on the stress space does not depend on the deformation path, it can be represented by a single limit line. Therefore, by using this as a breakage determination criterion, breakage of the stretch flange portion including one or more deformation path changes can be determined with high accuracy.

  According to the present invention, when determining the fracture limit of a thin plate in a process including one or more deformation path changes, it is possible to easily and efficiently obtain a fracture limit line and determine the fracture limit with high prediction accuracy. Become. According to the present invention, it is possible to quantitatively evaluate the risk of press forming and fracture at the time of collision, and it is possible to efficiently and highly accurately develop an automobile body considering materials, construction methods, and structures at the same time.

  Conventionally, the margin for fracture was often evaluated by the plate thickness reduction rate, but the method for evaluating fracture of materials using a forming limit diagram (FLD) due to the popularization of numerical simulation and the enhancement of post-processing software functionality. Has begun to be heavily used. Although FLD can be obtained by experiments such as the Nakajima method, the method is cumbersome and it is difficult to construct a database for various steel plate menus and plate thicknesses, so several prediction methods have been proposed. .

  For example, the post processing function of general-purpose software incorporates a method (see Non-Patent Document 1) in which Hiller's local constriction model and Swift's diffusion constriction model are added with Keeler's plate thickness correction rule of thumb. However, the predicted values obtained by these theories can be predicted with relatively high accuracy for aluminum and mild steel sheets, but over-evaluated on the uniaxial tension side for steel sheets of 440 MPa class or higher in tensile strength, and equal biaxial tension. Because it is underestimated on the side, it is not suitable for the development of an automobile body that uses a lot of high-strength steel plates as at present.

  In addition, it is known that FLD changes greatly depending on the deformation path, and plastic deformation in which the deformation path changes greatly, such as collision of automobile body parts that have undergone pre-deformation in press molding or press molding. A high prediction accuracy cannot be expected as a process fracture evaluation method. Recently, however, Kuwahara et al. (See Non-Patent Documents 2 and 3), for aluminum extruded materials and mild steel plates, use the fracture limit line expressed in the stress space to set the fracture limit regardless of the path of deformation. It is verified by experiment and analysis that it can be expressed almost uniquely. These findings relate to aluminum and mild steel sheets, and are not clarified for steel sheets with a tensile strength of 440 MPa or higher.

Therefore, the present inventors have conducted detailed experiments on a high-strength steel sheet having a tensile strength of 440 MPa or more, and have for the first time thought of the following matters.
(1) FLD of the strain space obtained by the proportional load path defines the stress-strain curve and material thickness obtained from the uniaxial tensile test, or the stress-strain curve and material thickness and stress increment dependency. Prediction can be performed with high accuracy using the parameter Kc, whereby an FLD database in a strain space can be easily and efficiently constructed for various types of steel plate menus and plate thicknesses.
(2) Fracture determination in a process including one or more deformation path changes is possible by converting FLD in a strain space obtained by this proportional load path into stress space and determining fracture in the stress space.

  Hereinafter, the present invention will be described in detail based on examples.

の関数式にフィッティングしたときに得られる材料パラメータを表す。比例負荷実験における破断限界歪みは、スクライブドサークル径を6mmとし、単軸引張、中島法（テフロン（登録商標）シートを用いた球頭張出し）、液圧バルジ試験での破断歪みを測定した。
図３に、上記の実験により測定した歪み空間の破断限界線を含むＦＬＤを示す。 Example 1
First, a method for experimentally measuring the FLD of the distortion space will be described.
The fracture limit strain was measured by a proportional load experiment for a steel plate made of a metal material having the mechanical characteristic values and material parameters shown in Table 1 below. Here, t is the thickness of the thin plate, YP is yield strength, TS is tensile strength, U.El the uniform elongation, El extends all, r _m represents the average r value (Lankford value, the rolling direction of the r If the value is r0, the r value in the 45 ° direction relative to the rolling direction is r45, and the r value in the 90 ° direction relative to the rolling direction is r90, then r _m = (r0 + 2r45 + r90) / 4. ), K, ε ₀ , n are stress-strain curves obtained from uniaxial tensile tests

The material parameters obtained when fitting to the functional equation The fracture limit strain in the proportional load experiment was determined by measuring the fracture strain in a uniaxial tension, Nakajima method (bulb head extension using a Teflon (registered trademark) sheet), and hydraulic bulge test with a scribed circle diameter of 6 mm.
FIG. 3 shows the FLD including the fracture limit line of the strain space measured by the above experiment.

を求めるためのデータを採取するが、試験方法としては単軸引張試験が簡便であり好ましい。単軸引張試験から得られる応力―歪み曲線から、

として適当な材料パラメータを含む関数式にフィッティングして材料パラメータを決定すればよい。近似の精度が高く、薄鋼板の数値シミュレーションでよく用いられるｎ乗硬化則を用いれば

で表現できる。 Next, a method for theoretically estimating the fracture limit line of the strain space from the mechanical property values of the material will be described.
FLD estimation methods include the combined use of Hill's local constriction model and Swift's diffusion constriction model, and the Stälen-Rice model (1975, J. Mech. Phys. Solids, 23, 421). It is obtained by correcting the influence of. A specific calculation method will be described below. First,

The data for obtaining the above is collected, but the uniaxial tensile test is preferable as the test method. From the stress-strain curve obtained from the uniaxial tensile test,

The material parameters may be determined by fitting to a functional expression including appropriate material parameters. If the approximation power is high and the n-thickness hardening rule, which is often used in numerical simulation of thin steel sheets, is used

Can be expressed as

を用いると、Hillの局部くびれは

Swiftの拡散くびれは

で与えられる。ただし、Hillの理論は2軸引張では局部くびれが得られないため、

の範囲で用い、ρ＞０の範囲ではSwiftの拡散くびれを適用する。図３では、理論的に計算した局部くびれ限界を、板厚をｔ₀（ｍｍ）として、Keelerの経験則

を用いて板厚の影響を補正したＦＬＤを示す。 The fracture limit strain is the nth power hardening law and the yield surface.

With Hill, the local constriction is

Swift's diffuse constriction

Given in. However, since Hill's theory does not allow local necking with biaxial tension,

In the range of ρ> 0, the Swift diffusion constriction is applied. In Fig. 3, Keeler's empirical rule, where the theoretically calculated local constriction limit is the thickness t ₀ (mm).

The FLD which corrected the influence of plate | board thickness using is shown.

で与えられる。 Swift's diffusional constriction tends to estimate the fracture limit near equal biaxial tension, and needs to be improved. Therefore, it is preferable to use the Stälen-Rice model, which is an extension of Hill's local constriction model based on the bifurcation theory. The Stälen-Rice model uses the n-th power hardening law and the yield surface in the incremental representation of the total strain theory for the Mises yield surface.

Given in.

FIG. 4 shows the FLD including the fracture limit line of the strain space calculated using the Stälen-Rice model.
Although there is a significant improvement in prediction accuracy over Swift's diffusional constriction model, it is difficult to ensure sufficient accuracy. Ito et al. (See Non-Patent Document 4) found that the stress increment tensor and the plastic strain increment tensor do not correspond one-to-one with the Mises' second-order yield function as a plastic potential. On the other hand, in order to overcome the drawback that the plastic strain increment direction does not follow, a constitutive equation in which the direction of the plastic strain increment tensor depends on the stress increment tensor is proposed. In this constitutive equation, the parameter Kc that defines the stress increment dependency of the plastic strain increment is required, but the physical background of Kc is unclear, and no parameter derivation method has been proposed.

Therefore, as a result of experiments conducted on the 440 MPa to 980 MPa class high-strength steel sheets shown in Table 2 below, the present inventors have conceived for the first time the following matters.
(1) The FLD can be predicted with high accuracy by identifying the material parameter Kc based on the measured values of the fracture limit maximum principal strain ε ₁ and the fracture limit minimum principal strain ε ₂ in equal biaxial tensile deformation.
(2) Since Kc does not depend on the plate thickness, the minimum necessary Kc should be obtained for each material tensile strength and steel plate strengthening mechanism.

FIG. 5 shows the FLD calculated for the 590 MPa grade precipitation-strengthened steel sheet shown in Table 2 by calculating Kc by the above-described method and using the stress increment dependence rule based on the Stälen-Rice model.
As a matter of course, higher prediction accuracy can be ensured by correcting using the fracture limit strain ε ₁ ^* in plane strain measured by experiment instead of Keeler's plate thickness correction rule. However, it is more efficient to use Keeler's plate thickness correction law from the viewpoint that various steel plate menus and FLD databases for plate thicknesses can be constructed using only the stress-strain curve of the uniaxial tensile test of the material.

(Method of converting from the fracture limit line of strain space to the fracture limit line of stress space)
For the steel sheets shown in Table 1, the fracture limit line in the proportional load path was predicted by the method described above, and the fracture limit line under the deformation path change was subjected to 10% tension in the rolling direction as the primary deformation. After that, the rupture strain was measured by uniaxial tension, Nakajima method (bulb head extension using a Teflon (registered trademark) sheet), and hydraulic bulge test so that the maximum principal stress was 90 ° from the primary tensile direction.

  The transformation from strain space to stress space assumes (1) constant volume law, (2) Mises yield function, (3) isotropic hardening by work hardening law, (4) vertical law, and (5) plane stress. Can be converted.

より求めることができる。通常、成形解析や衝突解析で用いられている構成則では、変形の経路によらず相当塑性応力σ_eqは相当塑性歪みε_eqの一義的関数と仮定する等方硬化則を用いており、Swiftの加工硬化則を用いれば

で表現できる。加工硬化の関数としては例えば、相当塑性歪みの高次多項式やその他の形式を用いてもよいが、近似の精度が高く、薄鋼板の数値シミュレーションでよく用いられるSwiftの式を用いるのが好ましい。相当塑性歪みε_eqは、例えば降伏曲面にMisesの降伏関数を用いれば

として表すことができる。 A specific method for converting the fracture limit line of the strain space into the stress space will be described below.
FLD of strain space is a diagram showing the maximum principal strain epsilon ₁₁ to give fracture limit for each minimum principal strain epsilon _22, plate thickness strain epsilon ₃₃ These and constant volume law

It can be obtained more. Normally, the constitutive law used in forming analysis and collision analysis uses the isotropic hardening rule that assumes that the equivalent plastic stress σ _eq is a unique function of the equivalent plastic strain ε _eq regardless of the deformation path. If the work hardening law of

Can be expressed as As the work hardening function, for example, a high-order polynomial of equivalent plastic strain or other forms may be used, but it is preferable to use the Swift equation that has high approximation accuracy and is often used in numerical simulation of thin steel sheets. Equivalent plastic strain ε _eq can be obtained, for example, by using Mises' yield function for the yield surface.

Can be expressed as

  Note that a sophisticated anisotropic yield function may be used if necessary, but since there are many parameters and it is necessary to consider the direction in the plate surface during processing, the cost of improving accuracy is complicated. However, the yield function assuming in-plane isotropic properties is sufficient for practical use.

により得られる。最後に平面応力(σ₃₃＝０)を仮定することで応力成分σ_ijは

より得られる。 Next, the deviation stress component σ _ij ^′ is the vertical law of the plastic strain increment for the yield surface shown in FIG.

Is obtained. Finally, assuming the plane stress (σ ₃₃ = 0), the stress component σ _ij is

More obtained.

  FIG. 7 shows the result of converting the FLD predicted by the above-described method and the fracture limit strain under the deformation path change measured by the experiment into the stress space. In the FLD of the strain space, the fracture limit varies greatly depending on the deformation path, but the fracture limit line expressed in the stress space can be expressed by a single fracture limit line regardless of the deformation path. Therefore, the fracture limit line of the material passing through a plurality of plastic deformation paths may be obtained by converting the FLD of the strain space obtained by the proportional load path into the stress space. Practically, a variety of steel plate menus and a database of fracture limit lines related to sheet thickness are obtained from the strain limit diagram (FLD) of the strain space from the stress-strain curve obtained from the uniaxial tensile test and the sheet thickness of the material. The break limit line can be obtained by converting to the stress space.

  Furthermore, as a result of experiments conducted on the high strength steel sheets of 440 MPa to 980 MPa class shown in Table 2, the present inventors have obtained a single fracture limit line in a wide range regardless of the tensile strength and strengthening mechanism of the material. Was revealed. By using the fracture limit line described in this stress space, it is possible to evaluate the fracture of plastic deformation processes in which the deformation path changes greatly, such as collision of automobile body parts that have undergone pre-deformation in press molding or press molding. It can be predicted with high accuracy.

(Example 2)
Further, a method for experimentally measuring the hole expansion rate of the strain space will be described. The specimen is a 1.2 mm thick composite structure steel plate (Dual Phase) produced by cold rolling-continuous annealing, and has the mechanical properties shown in Table 3. Mechanical property values were obtained by tensile testing with an Instron type tester at a crosshead speed of 10 mm / min (strain rate of 3 × 10 ^-3 / s). The test specimen was a JIS5 specimen taken in parallel with the rolling direction. Using.

最大主歪みと最小主歪みの歪み空間では、等方性を仮定すれば、破断限界は、この穴広げ率を用いては以下で表すとこができる。

First, the specimen was sheared to a size of 200 mm × 200 mm, and a hole having a diameter of 25 mm was punched out at the center using a punch and a die. This base plate with a hole in the center is molded with a flat bottom punch with a diameter of 100mm and a die shoulder of R15mm until the hole edge breaks (Teflon (registered trademark) sheet lubrication). It was measured. An outline of the experiment is shown in FIG. At this time, if d is the hole diameter (mm) at the time of fracture and d ₀ is the hole diameter (mm) of the base plate, the elongation distortion (hole expansion ratio) of the hole edge is defined by the following equation.

In the strain space of the maximum principal strain and the minimum principal strain, if isotropic is assumed, the fracture limit can be expressed as follows using this hole expansion ratio.

を求めるためのデータを採取するが、試験方法としては単軸引張試験が簡便であり好ましい。単軸引張試験から得られる応力―歪み曲線から、

として適当な材料パラメータを含む関数式にフィッティングして材料パラメータを決定すればよい。通常、成形解析や衝突解析で用いられている構成則では、変形の経路によらず相当塑性応力σ_eqは相当塑性歪みε_eqの一義的関数と仮定する等方硬化則を用いており、Swiftの加工硬化則を用いれば

で表現できる。加工硬化の関数としては例えば、相当塑性歪みの高次多項式やその他の形式を用いてもよいが、近似の精度が高く、薄鋼板の数値シミュレーションでよく用いられるSwiftの式を用いるのが好ましい。 Next, a method for converting the mechanical property value of the material into the fracture limit of the stress space will be described. First,

The data for obtaining the above is collected, but the uniaxial tensile test is preferable as the test method. From the stress-strain curve obtained from the uniaxial tensile test,

The material parameters may be determined by fitting to a functional expression including appropriate material parameters. Normally, the constitutive law used in forming analysis and collision analysis uses the isotropic hardening rule that assumes that the equivalent plastic stress σ _eq is a unique function of the equivalent plastic strain ε _eq regardless of the deformation path. If the work hardening law of

Can be expressed as As the work hardening function, for example, a high-order polynomial of equivalent plastic strain or other forms may be used, but it is preferable to use the Swift equation that has high approximation accuracy and is often used in numerical simulation of thin steel sheets.

より求めることができる。相当塑性歪みε_eqは、例えば降伏曲面にMisesの降伏関数を用いれば、

として表すことができる。なお、必要に応じて高度な異方性降伏関数を用いても良いが、パラメータが多く、処理の際に板面内の方向まで考慮する必要が生じるため、煩雑な割には精度の向上代が十分ではなく、実用上は面内等方性を仮定した降伏関数で十分である。
更に、応力空間への変換は、この穴広げ率の真歪みε_０と相当応力σ_eqと相当塑性歪みε_eqの関係式、例えば、Swiftの加工硬化則

を用いればよい。次に偏差応力成分σ_ij ^'は、図６に示す降伏曲面に対する塑性歪み増分の垂直則

により得られる。最後に平面応力(σ₃₃＝０)を仮定することで応力成分σ_ijは

より得られる。 Thickness strain ε ₃₃ is the equation (3) and constant volume

It can be obtained more. Equivalent plastic strain ε _eq is, for example, using Mises' yield function for the yield surface:

Can be expressed as Note that a sophisticated anisotropic yield function may be used if necessary, but since there are many parameters and it is necessary to consider the direction in the plate surface during processing, the cost of improving accuracy is complicated. However, the yield function assuming in-plane isotropy is sufficient in practice.
Further, the conversion to the stress space is performed by the relational expression of the true strain ε ₀ of the hole expansion rate, the equivalent stress σ _eq, and the equivalent plastic strain ε _eq , for example, Swift's work hardening law.

May be used. Next, the deviation stress component σ _ij ^′ is the vertical law of the plastic strain increment for the yield surface shown in FIG.

Is obtained. Finally, assuming the plane stress (σ ₃₃ = 0), the stress component σ _ij is

More obtained.

  FIG. 9 shows the fracture limit stress line obtained by the method described above. When using the conventional breaking limit line for the breaking limit (breaking criteria) in stretch flange deformation, due to the existence of strain gradient inward from the material end and the delay effect that does not break even if one circumferential direction satisfies the local constriction Although the forming limit height is estimated to be low, rupture can be predicted with good accuracy by using the rupture limit stress line obtained by the above-described method for rupture determination.

(Example 3)
FIG. 10 is a block diagram illustrating a main configuration of the fracture limit acquisition apparatus according to the first embodiment.
This fracture limit acquisition device is for determining a fracture limit of a thin plate in a process including one or more deformation path changes for a thin plate made of a metal material. The fracture limit line of a strain space obtained by a proportional load path is obtained. A conversion unit 1 that converts the fracture limit line of the stress space into a fracture limit line and a display unit 2 that displays the fracture limit line of the stress space obtained by the conversion unit 1 as a stress FLD are provided.

In this example, the fracture limit line of the strain space is measured experimentally. Specifically, the fracture limit line of the strain space is obtained by obtaining a plurality of in-plane strain ratios for a thin plate by a proportional load experiment, and then, the fracture limit maximum principal strain ε ₁ and the fracture limit minimum principal strain ε _{2 at} each strain ratio. It is obtained using the measured value.

を用いる。 When converting the fracture limit line of the strain space into the fracture limit line of the stress space, the conversion unit 1 uses the vertical law of the plastic strain increment in which the plastic strain increment direction is defined in a direction perpendicular to the yield surface. Perform the conversion. Specifically, as described above, Mises' yield function, which is a relational expression between the equivalent plastic strain ε _eq and each strain component ε _ij

Is used.

FIG. 11 is a flowchart illustrating the steps of the fracture limit acquisition method according to the first embodiment. In this example, as described above, the fracture limit line of the strain space is experimentally measured.
First, in conjunction with the type of sheet material input by the user, the conversion unit 1 converts the experimentally measured strain limit line of the strain space into a stress space fracture limit line using, for example, the Mises yield function. (Step S1).

  Subsequently, the fracture limit line of the stress space obtained in step S1 is displayed as stress FLD on the display unit 2 (step S2).

  As described above, according to this example, when determining the fracture limit of a thin plate in a process including one or more deformation path changes, a fracture limit line is easily and efficiently obtained, and the fracture limit is determined with high prediction accuracy. It becomes possible to judge. This example enables quantitative evaluation of the risk of press forming and fracture at the time of collision, and enables efficient and highly accurate development of an automobile body considering the material, construction method, and structure at the same time.

Example 4
FIG. 12 is a block diagram illustrating a main configuration of the fracture limit acquisition apparatus according to the second embodiment. The same components as those in FIG. 10 of the first embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.
This fracture limit acquisition device is for determining a fracture limit of a thin plate in a process including one or more deformation path changes for a thin plate made of a metal material, and estimating a fracture limit line of a strain space using a proportional load path. 1, an estimation unit 11, a conversion unit 1 that converts the fracture limit line of the obtained strain space into a fracture limit line of the stress space, and a fracture limit line of the stress space obtained by the conversion unit 1 is displayed as a stress FLD The display unit 2 is provided.

と、局部くびれモデル

と、拡散くびれモデル

とを併用して歪み空間のくびれ発生限界を求め、上述したように、比例負荷経路で歪み空間の破断限界線を推定する。 The first estimation unit 11 is an approximate expression of a stress-strain curve obtained from a uniaxial tensile test.

And local constriction model

And diffusion constriction model

Is used together to determine the squeezing limit of the strain space, and as described above, the fracture limit line of the strain space is estimated by the proportional load path.

FIG. 13 is a flowchart illustrating each step of the fracture limit acquisition method according to the first embodiment.
First, the user inputs the material and mechanical characteristic values (t, YP, TS, El, U.El, r value, n-th power hardening law / Swift hardening law) of the thin plate.

  The first estimation unit 11 estimates the fracture limit line of the strain space through the proportional load path based on the mechanical characteristic value input by the user (step S11).

Subsequently, the conversion unit 1 uses the n-th power hardening law / Swift hardening rule input as the mechanical characteristic value and the fracture function of the strain space estimated by the first estimation unit 11 using, for example, the Mises yield function. The limit line is converted into a fracture limit line in the stress space (step S12).
Subsequently, the fracture limit line of the stress space obtained in step S1 is displayed as the stress FLD on the display unit 2 (step S13).

  Note that the strain FLD is estimated from a database of shipping test values (t, YP, TS, El, U.El, r value, stress-strain multi-line data), and the shipping test value (in the quality variation distribution within a predetermined standard). The stress FLD may be calculated from the upper limit value, the lower limit value, and the average value of the quality variation distribution.

  As described above, according to this example, when determining the fracture limit of a thin plate in a process including one or more deformation path changes, a fracture limit line is easily and efficiently obtained, and the fracture limit is determined with high prediction accuracy. It becomes possible to judge. This example enables quantitative evaluation of the risk of press forming and fracture at the time of collision, and enables efficient and highly accurate development of an automobile body considering the material, construction method, and structure at the same time.

(Modification)
Here, a modification of the second embodiment will be described. In this modification, as shown in FIG. 14, the second estimation unit 12 is provided instead of the first estimation unit 11 in the fracture limit acquisition apparatus of the second embodiment.

と、塑性歪み増分則として塑性歪み増分テンソルの方向が応力増分テンソルに依存する構成式と、塑性歪み増分テンソルの方向を規定する材料パラメータＫｃと、シュテーレン−ライスの局所くびれモデルとを用いて歪み空間のくびれ発生限界を求め、比例負荷経路で歪み空間の破断限界線を推定する。ここで、第２の推定部１２は、上述したように、１つ以上の破断限界最大主歪みε₁及び破断限界最小主歪みε₂の測定値に基づいて、前記材料パラメータＫｃを同定する。 Similar to the first estimation unit 11, the second estimation unit 12 estimates the fracture limit line of the strain space in the proportional load path.

And a constitutive equation in which the direction of the plastic strain increment tensor depends on the stress increment tensor as a plastic strain increment rule, a material parameter Kc that defines the direction of the plastic strain increment tensor, and a local constriction model of Stälen-Rice The limit of constriction in the space is obtained, and the fracture limit line of the strain space is estimated by the proportional load path. Here, as described above, the second estimation unit 12 identifies the material parameter Kc based on the measured values of one or more fracture limit maximum principal strains ε ₁ and fracture limit minimum principal strains ε ₂ .

  As described above, according to this example, compared with Example 2, it is possible to ensure better accuracy with respect to fracture prediction, and to obtain a fracture limit line more easily and efficiently, and to achieve high prediction. It is possible to determine the fracture limit with accuracy.

(Other embodiments to which the present invention is applied)
The functions of the constituent elements (excluding the display unit 3) constituting the fracture limit acquisition apparatus according to the first and second embodiments described above can be realized by operating a program stored in a RAM or ROM of a computer. Similarly, each step of the fracture limit acquisition method (steps S1 to S2 in FIG. 11, steps S11 to S13 in FIG. 13, etc.) can be realized by operating a program stored in a RAM or ROM of a computer. This program and a computer-readable storage medium storing the program are included in the present invention.

  Specifically, the program is recorded on a recording medium such as a CD-ROM or provided to a computer via various transmission media. As a recording medium for recording the program, besides a CD-ROM, a flexible disk, a hard disk, a magnetic tape, a magneto-optical disk, a nonvolatile memory card, or the like can be used. On the other hand, as the program transmission medium, a communication medium in a computer network system for propagating and supplying program information as a carrier wave can be used. Here, the computer network is a WAN such as a LAN or the Internet, a wireless communication network, or the like, and the communication medium is a wired line such as an optical fiber or a wireless line.

  Further, the program included in the present invention is not limited to the one in which the functions of the above-described embodiments are realized by the computer executing the supplied program. For example, such a program is also included in the present invention when the function of the above-described embodiment is realized in cooperation with an OS (operating system) or other application software running on the computer. Further, when all or part of the processing of the supplied program is performed by the function expansion board or function expansion unit of the computer and the functions of the above-described embodiment are realized, the program is also included in the present invention.

  For example, FIG. 15 is a schematic diagram illustrating an internal configuration of a personal user terminal device. In FIG. 13, reference numeral 1200 denotes a personal computer (PC) having a CPU 1201. The PC 1200 executes device control software stored in the ROM 1202 or the hard disk (HD) 1211 or supplied from the flexible disk drive (FD) 1212. The PC 1200 generally controls each device connected to the system bus 1204.

  Steps S1 to S2 in FIG. 11 of the third embodiment and steps S11 to S13 in FIG. 13 of the fourth embodiment are realized by a program stored in the CPU 1201, the ROM 1202, or the hard disk (HD) 1211 of the PC 1200.

  A RAM 1203 functions as a main memory, work area, and the like for the CPU 1201. A keyboard controller (KBC) 1205 controls instruction input from a keyboard (KB) 1209, a device (not shown), or the like.

  Reference numeral 1206 denotes a CRT controller (CRTC), which controls display on a CRT display (CRT) 1210. Reference numeral 1207 denotes a disk controller (DKC). The DKC 1207 controls access to a hard disk (HD) 1211 and a flexible disk (FD) 1212 that store a boot program, a plurality of applications, an editing file, a user file, a network management program, and the like. Here, the boot program is a startup program: a program for starting execution (operation) of hardware and software of a personal computer.

  Reference numeral 1208 denotes a network interface card (NIC) that exchanges data bidirectionally with a network printer, another network device, or another PC via the LAN 1220.

It is a shaping | molding limit diagram (FLD) used for description of a prior art. It is a forming limit diagram (FLD) used for explanation of a problem which the present invention tends to solve. It is a figure used for description of the Example of this invention, and is a shaping | molding limit diagram (FLD) measured by experiment. FIG. 5 is a diagram used for explaining an embodiment of the present invention, and forming considering the influence of the plate thickness by using the Keeler plate thickness correction law for the plastic instability limit line predicted by the Hill-Swift theory and the Stälen-Rice model. It is a limit diagram (FLD). It is a figure used for description of the Example of this invention, and is a shaping | molding limit diagram (FLD) estimated using the stress increase dependence law based on the Stären-Rice model. It is the figure used for description of the Example of this invention, and is the figure explaining the conversion from distortion to stress. It is a figure used for explanation of an example of the present invention, and it shows that the fracture limit line of the stress space can be expressed by a single curve, while the fracture limit of the strain space FLD changes greatly depending on the deformation path. It is a figure. It is a figure used for description of the Example of this invention, and is a figure explaining the experiment method. It is a figure used for description of the Example of this invention, and is a figure which shows the fracture | rupture limit stress line which expressed the hole expansion rate in stress space. It is a block diagram which shows the main structures of the fracture limit acquisition apparatus by Example 1. FIG. It is a flowchart which shows each step of the fracture | rupture limit acquisition method by Example 1. FIG. It is a block diagram which shows the main structures of the fracture limit acquisition apparatus by Example 2. FIG. FIG. 6 is a flowchart showing steps of a fracture limit acquisition method according to Example 2. It is a block diagram which shows the main structures of the fracture | rupture limit acquisition apparatus by the modification of Example 2. FIG. It is a schematic diagram which shows the internal structure of a personal user terminal device.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Conversion part 2 Display part 11 1st estimation part 12 2nd estimation part

Claims (31)

A method for obtaining a break limit line used for determining a break limit of a thin plate made of a metal material,
In determining the breaking limit of the thin plate in the process including one or more deformation path changes,
A method for obtaining a fracture limit, comprising: converting a fracture limit line in a strain space obtained by a proportional load path into a fracture limit line in a stress space.   When the fracture limit line of the strain space is converted into the fracture limit line of the stress space, a plastic strain increment vertical law is used in which the plastic strain increment direction is defined in a direction perpendicular to the yield surface. The fracture limit acquisition method according to claim 1. When using the vertical law of plastic strain increment, the relational expression between the equivalent plastic strain ε _eq and each strain component ε _ij

The method for obtaining a fracture limit according to claim 2, wherein: When obtaining the fracture limit line of the strain space in the proportional load path, after obtaining a plurality of in-plane strain ratios for the thin plate by proportional load experiments, the fracture limit maximum principal strain ε ₁ and the fracture limit in each strain ratio The method for obtaining a fracture limit according to any one of claims 1 to 3, wherein a measured value of the minimum principal strain ε ₂ is used. When obtaining the fracture limit line of the strain space in the proportional load path,

The fracture limit obtaining method according to any one of claims 1 to 3, wherein a squeezing limit of the strain space is obtained by using together. When obtaining the fracture limit line of the strain space in the proportional load path,

As a plastic strain increment rule, a constitutive equation in which the direction of the plastic strain increment tensor depends on the stress increment tensor,
A material parameter Kc defining the direction of the plastic strain increment tensor;
The fracture limit acquisition method according to any one of claims 1 to 3, wherein a limit of occurrence of the necking of the strain space is obtained using a Stären-Rice local necking model. One or more based on the measurement values of fracture limit maximum principal strain epsilon ₁ and fracture limit minimum principal strain epsilon _2, fracture limit obtaining method according to claim 6, wherein the identification of the material parameters Kc. Based on the constriction limit,
A thickness t ₀ (mm) of the thin plate;
A stress-strain curve obtained from a uniaxial tensile test;

The fracture limit acquisition method according to claim 5 or 6, wherein the fracture limit strain of the strain space is obtained using the method.   The fracture limit obtaining method according to any one of claims 1 to 8, wherein the thin plate is made of a high-strength material having a tensile strength of 440 MPa or higher.   10. The fracture limit acquisition method according to claim 1, wherein elongation strain obtained from the hole expansion test is converted into a stress space, and fracture is determined in the stress space. For a thin plate made of a metal material, a fracture limit acquisition device for determining a fracture limit of the thin plate in a process including one or more deformation path changes,
A breakage limit acquisition apparatus comprising a conversion means for converting a breakage limit line of a strain space obtained by a proportional load path into a breakage limit line of a stress space.   The converting means uses a plastic strain increment vertical law in which a plastic strain increment direction is defined in a direction perpendicular to a yield surface when transforming the fracture limit line of the strain space into a fracture limit line of the stress space. The breaking limit acquisition device according to claim 11. When the conversion means uses the vertical law of the plastic strain increment, the relational expression between the equivalent plastic strain ε _eq and each strain component ε _ij

The breaking limit acquisition device according to claim 12, wherein: The fracture limit line of the strain space is obtained by determining a plurality of in-plane strain ratios for the thin plate by a proportional load experiment, and then measuring the fracture limit maximum principal strain ε ₁ and the fracture limit minimum principal strain ε ₂ at each strain ratio. The breakage limit acquisition apparatus according to any one of claims 11 to 13, wherein the breakage limit acquisition apparatus is obtained using the above.

14. The method further comprises: first estimation means for obtaining a squeezing limit of the strain space by using the same, and estimating a fracture limit line of the strain space by the proportional load path. Breakage limit acquisition device according to item.

As a plastic strain increment rule, a constitutive equation in which the direction of the plastic strain increment tensor depends on the stress increment tensor,
A material parameter Kc defining the direction of the plastic strain increment tensor;
And a second estimation means for obtaining a necking limit of the strain space using a Stären-Rice local necking model and estimating a fracture limit line of the strain space using the proportional load path. Item 14. The breaking limit acquisition device according to any one of Items 11 to 13. Said second estimation means, based on one or more measurements of fracture limit maximum principal strain epsilon ₁ and fracture limit minimum principal strain epsilon _2, in claim 16, wherein the identification of the material parameters Kc The breaking limit acquisition device described. The first estimating means is based on the constriction occurrence limit,
A thickness t ₀ (mm) of the thin plate;
A stress-strain curve obtained from a uniaxial tensile test;

The fracture limit acquisition apparatus according to claim 15, wherein the fracture limit strain of the strain space is obtained using a squeeze. The second estimating means uses the constriction occurrence limit as a reference,
A thickness t ₀ (mm) of the thin plate;
A stress-strain curve obtained from a uniaxial tensile test;

The fracture limit acquisition device according to claim 16, wherein a fracture limit strain of the strain space is obtained using a squeeze.   The fracture limit acquiring apparatus according to any one of claims 11 to 19, wherein the thin plate is made of a high-strength material having a tensile strength of 440 MPa or more.   The fracture limit acquisition apparatus according to any one of claims 11 to 13, wherein the elongation strain obtained from the hole expansion test is converted into a stress space, and the fracture is determined in the stress space. When determining the breaking limit of the thin plate in the process including one or more deformation path changes for the thin plate made of a metal material,
A program for causing a computer to execute a procedure for converting a fracture limit line of a strain space obtained by a proportional load path into a fracture limit line of a stress space.   In the procedure of converting the fracture limit line of the strain space into the fracture limit line of the stress space, a vertical law of plastic strain increment is used in which the plastic strain increment direction is defined in a direction perpendicular to the yield surface. The program according to claim 22. When using the vertical law of plastic strain increment, the relational expression between the equivalent plastic strain ε _eq and each strain component ε _ij

24. The program according to claim 23, wherein: The fracture limit line of the strain space in the proportional load path is obtained by determining a plurality of in-plane strain ratios for the thin plate by a proportional load experiment, and then the fracture limit maximum principal strain ε ₁ and the fracture limit minimum principal strain at each strain ratio. The program according to any one of claims 22 to 24, wherein a measured value of ε ₂ is obtained. Prior to the procedure of converting the fracture limit line of the strain space to the fracture limit line of the stress space,

The program according to any one of claims 22 to 24, for causing a computer to execute a procedure for obtaining a squeezing limit of a strain space by using the same, and estimating a fracture limit line of the strain space in the proportional load path. . Prior to the procedure of converting the fracture limit line of the strain space to the fracture limit line of the stress space,

As a plastic strain increment rule, a constitutive equation in which the direction of the plastic strain increment tensor depends on the stress increment tensor,
A material parameter Kc defining the direction of the plastic strain increment tensor;
25. A method according to claim 22 for causing a computer to execute a procedure of obtaining a necking limit of the strain space using a Stären-Rice local necking model and estimating a fracture limit line of the strain space in the proportional load path. The program according to any one of the above items. One or more based on the measured value of the breakage threshold maximum principal strain epsilon ₁ and fracture limit minimum principal strain epsilon _2, the program according to claim 27, wherein the identification of the material parameters Kc. Based on the constriction limit,
A thickness t ₀ (mm) of the thin plate;
A stress-strain curve obtained from a uniaxial tensile test;

28. The program according to claim 26, wherein the fracture limit strain of the strain space is obtained using the program.   The program according to any one of claims 22 to 24, wherein the elongation strain obtained from the hole expansion test is converted into a stress space, and the fracture is determined in the stress space.   The computer-readable recording medium which recorded the program of any one of Claims 22-30.

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