JP2007232715A - Method and device for breaking estimation, program and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily and efficiently calculate a breaking limit line when the breaking limit of a stretch flange part is judged in a thin sheet in a step containing at least one deformation route change not only to estimate breaking with high precision but also to evaluate the dangerousness of breaking when press molding or collision. <P>SOLUTION: A breaking limit stress line, the hole widening ratio of which is converted to stress, is set to the criteria of breaking, and data acquired from the analysis of a numerical value using a finite-element method and the relation of the breaking limit stress line are compared with each other to quantitatively evaluate the breaking dangerousness of a material. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method and an apparatus for predicting a fracture of a thin plate made of a metal material, a program, and a recording medium, and is particularly suitable as a fracture judgment criterion for 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 the maximum principal strain that gives the 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.

2004, Plasticity and processing 45, 123 2004, CAMP-ISIJ 17, 1063

  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, (1) In the case of a path change where biaxial tensile deformation is applied after uniaxial tension pre-strain, compared to the fracture limit line when there is no change in the deformation path and a linear path change is applied, the fracture limit line In the case of (3) the path change that applies uniaxial tension after biaxial tension pre-strain, etc. or (4) the path change that applies plane strain tension deformation after bi-axial tension pre-strain, etc., the fracture limit line decreases. It has become 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.

  Further, the stretch flange break occurs when the elongation strain in the circumferential direction of the material end 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 breakage, even if the material end reaches the plastic instability condition and local constriction (thickness constriction) occurs, the material and the inner material excluding the end do 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 break, a large number of plate thickness constrictions occur in the circumferential direction of the material end portion, so that the break 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 thickness constriction increases, the effect of this stress relaxation decreases, and when the deformation proceeds further, the next sheet thickness constriction occurs away from the initial 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 grows and does not break, because it is constrained by a material with little distortion and does not satisfy 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 has a technical problem to solve the above-described problems of the prior art, and when predicting the occurrence of breakage of a thin plate in a process including one or more deformation path changes, the break limit line is easily and efficiently determined. It is possible to predict the occurrence of rupture with high prediction accuracy and quantitatively evaluate the risk of rupture during press molding and collision. An object of the present invention is to provide a fracture prediction method and apparatus, a program, and a recording medium that realize efficient and highly accurate development.

  The fracture prediction method of the present invention is a fracture prediction method for evaluating the fracture limit of a thin plate made of a metal material, and predicts the occurrence of fracture of the thin plate in a plastic deformation process according to one or more deformation path changes. At this time, a procedure for converting a fracture limit line in a strain space into a fracture limit line in a stress space and a procedure for predicting the occurrence of the fracture using the obtained fracture limit line in the stress space are included.

  The fracture prediction device of the present invention is a fracture prediction device that evaluates the fracture limit of a thin plate made of a metal material, and predicts the occurrence of fracture of the thin plate in a plastic deformation process according to one or more deformation path changes. Conversion means for converting the fracture limit line of the strain space into a fracture limit line of the stress space, and prediction means for predicting the occurrence of the fracture using the obtained fracture limit line of the stress space.

  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. By using a hole expansion ratio that has a good correlation with the stretch flange rupture limit for fracture criteria, and by determining fracture in a stress space that can take into account the influence of deformation history, not strain space, with high accuracy Clarified what can be predicted.

  According to the present invention, when predicting the occurrence of fracture of a thin plate in a process including one or more deformation path changes, the fracture limit line is easily and efficiently obtained, and the presence or absence of fracture is predicted with high prediction accuracy. It becomes possible. This makes it possible to quantitatively evaluate the risk of press forming and breakage at the time of collision, and realizes efficient and highly accurate development of an automobile body that simultaneously considers materials, construction methods, and structures.

  The margin for breakage at the time of formability evaluation is generally determined using a plate thickness reduction rate or FLD, which can also be used for fracture prediction in a collision analysis. Of these, it is known that FLD changes greatly depending on the deformation path, and plasticity such that 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 method for evaluating the fracture of the deformation process.

  Recently, however, Kuwahara et al. (See Non-Patent Documents 1 and 2), for aluminum extruded materials and mild steel sheets, 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 are related to aluminum and mild steel sheets, and are not clarified for steel sheets with a tensile strength of 440 MPa or higher. Can not.

Therefore, the present inventors have conceived for the first time the following matters.
(1) When a detailed experiment is performed on a high-strength steel sheet having a tensile strength of 440 MPa or more and the fracture limit line expressed in the stress space is used, it can be expressed by a single fracture limit line regardless of the deformation path. (2) By using the fracture limit line indicated in the stress space, the plastic deformation process breaks such that the deformation path changes greatly, such as the collision of a car body part that has undergone pre-deformation in press molding or press molding. The evaluation can be predicted with high accuracy.

  The general configuration of the present invention will be described below.

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。 Example 1
First, a method for obtaining the fracture limit line of the stress space will be described. For the steel sheets shown in Table 1 below, (1) the breaking limit strain in the proportional load path and (2) the breaking limit strain under the deformation path change were measured. 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 When the value is r0, the r value in the 45 ° direction with respect to the rolling direction is r45, and the r value in the 90 ° direction with respect to the rolling direction is r90, r _m = (r ₀ + 2r ₄₅ + r ₉₀ ) / 4. ), K, ε ₀ , and 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 path was measured with a scribed circle diameter of 6 mm, uniaxial tension, Nakajima method (bulb head extension using Teflon (registered trademark) sheet), and hydraulic bulge test. . On the other hand, the fracture limit line under the change of the deformation path is uniaxial tension, Nakajima so that the maximum principal stress is 90 ° from the primary tension direction after applying 10% tension in the rolling direction as the primary deformation. The breaking strain was measured by the method.

  Strain to stress is converted by assuming (1) constant volume rule, (2) Mises yield function, (3) isotropic hardening by work hardening law, (4) vertical law, and (5) plane stress. be able to. A specific method for converting the fracture limit line of the strain space into the stress space will be described below.

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。 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.

として表すことができ、また面内等方性を仮定したHillの2次降伏関数を用いれば、

により得られる。Hillの２次降伏関数を用いる場合には塑性異方性パラメータｒ値が必要であり、具体的には圧延方向から０゜、４５゜、９０゜の方向のｒ値（ｒ₀，ｒ₄₅，ｒ₉₀）から、ｒ＝（ｒ₀＋２ｒ₄₅＋ｒ₉₀）／４により得られる。 Equivalent plastic strain ε _eq is, for example, using Mises' yield function for the yield surface:

And using Hill's quadratic yield function assuming in-plane isotropy,

Is obtained. When Hill's quadratic yield function is used, a plastic anisotropy parameter r value is necessary. Specifically, r values (r ₀ , r ₄₅ , r ₀ , 0 °, 45 °, 90 ° from the rolling direction). r ₉₀ ), r = (r ₀ + 2r ₄₅ + r ₉₀ ) / 4.

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. In any yield function, by using the equivalent plastic strain ε _eq obtained by integrating the equivalent plastic strain increment dε _eq with the strain path and the work hardening rule, the equivalent plastic stress σ _eq considering the deformation path change can be obtained.

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 isotropic hardening of the yield surface shown in FIG.

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

More obtained.

座標変換テンソルをRとすると、(1)実験座標系で計測した歪み成分ε_ijは座標変換則により材料座標系を基準座標とした歪み成分

へ変換できる。次に、(２)材料座標系を基準座標系としてモデル化されている降伏関数と垂直則から

を求め、最後に、(３)座標変換則を用いて実験座標系を基準座標とした応力成分

を求めることができる。 In addition, as shown in FIG. 4, when the main axis | shaft of distortion and a rolling direction do not correspond, the coordinate transformation operation shown below is required. In the figure, x _i represents x ₁ axis // RD is a coordinate axis of the material coordinate system, x ₂ axis // TD, the x ₃ axis // ND, X _i represents the main axis of the strain at n-order modified.

If the coordinate transformation tensor is R, (1) the strain component ε _ij measured in the experimental coordinate system is the strain component with the material coordinate system as the reference coordinate according to the coordinate transformation rule

Can be converted. Next, (2) from the yield function and the vertical law modeled with the material coordinate system as the reference coordinate system

Finally, (3) Using the coordinate transformation rule, the stress component with the experimental coordinate system as the reference coordinate

Can be requested.

FIG. 5 shows the FLD measured by experiment and the fracture limit line obtained by converting the FLD into the stress space of the maximum principal stress and the minimum principal stress by the method described above.
The FLD in the strain space depends on the deformation path, and the fracture limit line changes greatly, but the fracture limit line described in the stress space becomes a single fracture limit line.

  Furthermore, as a result of experiments conducted on the high strength steel sheets of 440 MPa to 980 MPa class shown in Table 2 below, the present inventors have found a single fracture limit line in a wide range regardless of the tensile strength and strengthening mechanism of the material. Clarified that 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.

  Of course, a fracture limit line obtained by converting FLD measured by an experimental method other than the Nakajima method into a stress space may be used, a Hill's local constriction model, a Swift's diffusion constriction model, the Marciniak-Kuczynski method, A fracture limit line obtained by converting a theoretical FLD such as a Storen-Rice model into a stress space may be used for fracture prediction.

Next, a method for evaluating the fracture limit will be described.
In order to predict material breakage by numerical simulation using the finite element method (FEM), there are the following technical problems.
(1) Since the FLD measured by the experiment is strongly affected by the distance between the scores and the frictional state, when this is used as a fracture criterion, it is necessary to correct it according to the analysis conditions of the numerical simulation.
(2) In numerical simulation, the increase in strain up to uniform deformation can be accurately simulated, but in order to simulate a local constriction that occurs in the region of the plate thickness or a shear band in which strain is localized in a narrower region Finite elements must be sufficiently subdivided, and it is difficult to predict with the current computational capabilities.
(3) In the material constitutive law that is standardly adopted in general-purpose software, the localization of strain is delayed. Therefore, when the measured FLD is used as a criterion for fracture determination, an evaluation on the dangerous side is given.

  As a result of intensive studies on these problems, the present inventors have clarified a fracture criterion suitable for numerical simulation. FEM numerical simulation of ball head overhang forming was performed on the steel sheets shown in Table 1, and the effects of element size and material constitutive equation on the strain localization process were investigated.

FIG. 6 shows the relationship between the punch stroke and the maximum principal strain introduced by press molding.
From the initial stage of molding to the punch stroke of about 25 mm, the effect of element size and material constitutional expression hardly appears, but after 25 mm where strain localization starts, these effects become significant.

FIG. 7 shows a comparison of prediction accuracy when a numerical simulation is performed under various analysis conditions and the FLD obtained from the experiment and the local necking limit are used as the fracture criterion.
When the measured FLD is used as the fracture criterion, since the strain localization process cannot be simulated accurately, the fracture prediction accuracy is not high. On the other hand, when the local constriction occurrence limit is used as the fracture limit, it can be predicted with relatively high accuracy regardless of the element size and the material composition formula to be used, and an evaluation on the safe side can be obtained. This is because ductile fracture of thin steel sheet occurs at a position where deformation is localized due to local constriction, and when local constriction occurs, it breaks in an extremely short time. Suggests good.

  The local constriction limit can be handled in the framework of plastic instability and can be predicted by theoretical FLDs such as Hill's local constriction model, Swift's diffusion constriction model, Marciniak-Kuczynski method, and Stären-Rice model.

  As shown in this example, the present inventors have conducted intensive research.As a result, when evaluating fracture by numerical analysis simulation using the finite element method, the fracture limit line obtained by converting the constriction start line in the strain space into the stress space. It was conceived that high prediction accuracy can be secured by using as a criterion for judging fracture.

Next, an example of a method for evaluating the fracture limit will be described.
An example of fracture prediction in a non-linear path is shown in which the steel sheet shown in Table 1 is subjected to a tensile deformation of 10% in the rolling direction as a primary deformation and then subjected to plane strain deformation by ball head overhang forming.
FIG. 8 shows the relationship between the stress history of the forming process obtained by the numerical simulation and the fracture limit line obtained by converting the constriction start line in the strain space into the stress space.

  When the dynamic explicit method is used for the numerical simulation, the obtained stress is not repeatedly calculated within the time step, and increases while greatly oscillating because the propagation of the stress wave is solved in minute time steps. It is difficult to ensure high prediction accuracy by a method for evaluating the fracture by comparing the positional relationship between this stress and the fracture limit stress.

  As a result of diligent research, the present inventors have come up with a method for determining fracture with high accuracy by using a dynamic explicit method for numerical simulation and converting plastic strain into stress by post-processing to avoid stress vibration. .

FIG. 9 shows the result of predicting fracture by the method of the present invention.
In the conventional fracture prediction method using FLD, it is difficult to predict with high accuracy because the fracture limit line greatly changes depending on the deformation path, but it is good even when the deformation path changes by applying the present invention. It can be seen that the fracture can be predicted with accuracy. In the present invention, instead of numerical simulation using the finite element method, it is possible to evaluate fracture by comparing the positional relationship between the value obtained by converting the experimental strain measurement result into stress and the fracture limit line. .

Next, an example in which the fracture prediction method is applied to collision analysis will be described.
The fracture prediction method of the present invention was applied to a steel plate shown in Table 1 in a three-point bending collision analysis of a member having a hat cross section and a length of 900 mm shown in FIG.

  First, a hat-shaped drawing bending analysis was performed using a numerical simulation of a dynamic explicit method. FIG. 11 shows the result of the molding simulation. Next, a finite element model for collision analysis was created by performing spot welding processing (fixed relative displacement between two contacts) with a flat plate at a flange part at 30mm intervals.

  Furthermore, the obtained molding analysis result was reflected in this finite element model for collision analysis, and the collision analysis was performed by numerical simulation by the dynamic explicit method. When evaluating the fracture of a material in the collision process after press forming, the plate thickness and equivalent plastic strain, or the plate thickness and equivalent plastic strain, stress tensor, and strain tensor obtained by numerical simulation of press forming are the initial conditions for collision analysis. By taking over, the deformation history at the time of molding can be considered.

  As a matter of course, instead of numerical simulation, the thickness and equivalent plastic strain of the press-formed product are measured by experiment, and the deformation history at the time of molding is taken into account by taking any of these to the initial conditions of the collision analysis. be able to.

  In previous cases, we dealt with quasi-static plastic deformation processes such as press forming, but it is necessary to consider the high-speed deformation behavior of materials in collision analysis. Steel materials are known to have strain rate dependence, and it is known that deformation resistance increases when the deformation rate is high. At the ridgeline where deformation is concentrated at the time of automobile collision, the strain rate can reach up to 1000 / s, and accurate high-speed deformation behavior needs to be considered in order to ensure the accuracy of collision analysis prediction.

In general, when impact analysis is performed by numerical simulation using the finite element method, the Cowper-Symonds equation is used as a material model that represents an increase in stress according to the strain rate.
FIG. 12 shows the relationship between the equivalent plastic strain and the equivalent stress in accordance with the strain rate, and FIG. 13 shows the positional relationship between the dynamic fracture stress limit line in the stress space and the dynamic stress obtained from the collision simulation.

  When rupture is evaluated using dynamic stress obtained from a collision simulation, an infinite number of dynamic rupture stress limit lines are required according to the strain rate, and it is difficult to predict the rupture practically.

  As a result of diligent research to solve this problem, the present inventors have used the stress at the standard strain rate obtained by converting the plastic strain obtained from the collision simulation, and used the fracture limit (break criteria) used for fracture determination. It was conceived that only the breaking stress limit line at a single reference strain rate should be used. As a result of the examination, it was found that the reference strain rate is good as a quasi-static strain rate. Although the range of the quasi-static strain rate varies depending on the material, a fracture limit line measured in the range of 0.001 / s to 1 / s may be used in practice.

FIG. 14 shows the result of predicting fracture by the method of the present invention.
In conventional fracture prediction methods using FLD, it has been difficult to predict with high accuracy a plastic deformation process in which the deformation path changes greatly, such as a collision phenomenon after undergoing pre-deformation in press forming. It can be seen that by applying the invention, fracture can be predicted with good accuracy even in the collision process after press forming.

  As shown in the above examples, according to the present invention, it is possible to simulate the press forming and collision process of a thin steel plate by a finite element method, and quantitatively evaluate the risk of fracture from the obtained data. Here, the Cowper-Symonds equation is used as a representative example of the strain rate dependency of the deformation stress, but any constitutive equation that can take into account the strain rate dependency, such as the m-th power hardening equation, Johnson-Cook equation, etc. The effectiveness of the present invention remains unchanged.

(Example 2)
Hereinafter, as specific embodiments of the present invention, stretch flange breakage evaluation methods using the hole expansion ratio l in the stress space as criteria will be described.
The test material is a 1.2 mm thick composite structure steel plate (Dual Phase) manufactured 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.

  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. Furthermore, in order to use it as a criterion for fracture prediction in numerical simulation, the FLD was measured by the Nakajima method (bulb head projection using a Teflon (registered trademark) sheet).

  Subsequently, numerical simulation by dynamic explicit FEM was performed to verify the prediction accuracy of stretch flange breakage that breaks from the end of the material. The material parameters used in the numerical simulation were used in the experiment, and the tool was copied from the experiment. The analysis model is shown in FIG. The element size was 2 mm, which was the same as the distance between scores at the time of FLD measurement, and Hill's second-order anisotropic yield function was used as the yield function.

但し、dは破断時の穴径(mm)を、d₀は素板の穴径(mm)である。応力空間でのクライテリアへの変換は、この穴広げ率の真歪みε₀と相当塑性応力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。なお、相当塑性歪み増分ｄε_eqを歪み経路で積分した相当塑性歪みε_eqと加工硬化則を用いることで、変形経路変化を考慮した相当塑性応力σ_eqを求めることができる。 FIG. 17 shows a simulation result of stretch flange molding using a flat bottom punch, and FIG. 18 shows the relationship between the distance from the hole edge and the maximum principal strain. From these, it can be seen that a large strain is introduced into the hole edge of the material end and that a large strain gradient exists from the hole edge inward. In FIG. 19, the plastic strain obtained from the numerical simulation is converted into a stress space, the stress history plotted for each molding height, and the molding limit line measured in the proportional load path, the limit value in plane strain is equal to the n value. The relationship between the “neck generation limit stress line” obtained by offsetting in this way and the “neck generation limit stress line” converted into a stress space is shown. The stress at the hole edge reaches the constriction critical stress line at the molding height of 14 mm, which is a big difference from the molding limit height of 18.5 mm measured in the experiment. On the other hand, the fracture was evaluated in the stress space with the fracture criteria as the hole expansion ratio. The hole expansion rate is defined by the following equation.

However, d is the hole diameter at break a (mm), d ₀ is the hole diameter of the workpiece (mm). Conversion to criteria in the stress space is based on the relationship between the true strain ε ₀ of the hole expansion ratio, the equivalent plastic stress σ _eq, and the equivalent plastic strain ε _eq , for example, Swift's work hardening law

May be used. Incidentally, by using the equivalent plastic strain ε _eq obtained by integrating the equivalent plastic strain increment dε _eq with the strain path and the work hardening rule, the equivalent plastic stress σ _eq considering the deformation path change can be obtained.

  20 and 21 show the results of predicting fracture by the method of the present invention. When the conventional `` necking limit stress line '' is used for fracture criteria in stretch flange deformation, there is a strain gradient inward from the end of the material and a delay effect that does not break even if one circumferential direction satisfies the local neck Thus, it is understood that the fracture limit can be predicted with good accuracy by using a criterion in which the hole expansion rate is converted into a stress space for fracture determination.

(Example 3)
Hereinafter, specific embodiments will be described with reference to the drawings based on the above-described general configuration of the present invention.
FIG. 22 is a block diagram showing the main configuration of the fracture prediction device according to this embodiment.
This fracture prediction device predicts whether or not a thin plate breaks in a process including one or more deformation path changes for a thin plate made of a metal material, and estimates a fracture limit line of a strain space using a proportional load path. An estimator 1; a converter 2 that converts a rupture limit line of a strain space obtained by a proportional load path into a rupture limit line of a stress space; and a rupture determination unit that determines whether or not a rupture has occurred based on the rupture limit line of a stress space 3 and a display unit 4 for displaying a determination result or the like by the break determination unit 3.

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、比例負荷経路で歪み空間の破断限界線を推定する。 The estimation unit 1 is an approximate expression of a stress-strain curve obtained from a uniaxial tensile test, for example.

And local constriction model

And diffusion constriction model

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

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ようにしても良い。ここで、推定部１は、１つ以上の最大破断限界歪みε₁及び最小破断限界歪みε₂の測定値に基づいて、材料パラメータＫｃを同定する。 The estimation unit 1 is an approximate expression of a stress-strain curve obtained from a uniaxial tensile test.

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 Stalen-Rice It is also possible to obtain the squeezing limit of the space and estimate the rupture limit line of the strain space by the proportional load path. Here, the estimation unit 1 identifies the material parameter Kc based on the measured values of the one or more maximum breaking limit strain ε ₁ and the minimum breaking limit strain ε ₂ .

In this example, the case where the rupture limit line of the strain space is theoretically estimated using the estimation unit 1 is illustrated, but the rupture limit line of the strain space is experimentally measured without using the estimation unit 1. Also good. Specifically, the fracture limit line of the strain space is obtained by measuring a plurality of in-plane strain ratios for a thin plate by a proportional load experiment, and then measuring the maximum fracture limit strain ε ₁ and the minimum fracture limit strain ε ₂ at each strain ratio. Obtained using the value.

を用いる。 When converting the fracture limit line of the strain space to the fracture limit line of the stress space, the conversion unit 2 performs the above-described conversion using the vertical law of the yield surface as the incremental law of plastic strain. 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.

  The fracture determination unit 3 is evaluated by comparing the positional relationship between the fracture limit line of the stress space converted by the conversion unit 1 and the strain state of each part obtained from the simulation result of the plastic deformation process by the finite element method. However, when the strain in the deformation process reaches the limit strain, it is determined that the fracture or the risk is high. Here, a dynamic explicit method, which is one of the finite element methods, is used as a numerical analysis method. In this case, the plastic strain obtained by the dynamic explicit method is converted into stress and compared with the fracture limit line of the stress space.

  Instead of performing the above simulation, the fracture determination unit 3 converts the strain obtained from the deformation state of the thin plate evaluated by the experiment into stress, and uses the fracture limit line in the stress space to determine whether or not the fracture has occurred. You may make it evaluate quantitatively.

  Here, when high-speed deformation occurs in the thin plate as in the collision analysis of the automobile member, the fracture determination unit 3 performs numerical analysis in consideration of the speed dependency of the deformation stress of the thin plate. The obtained plastic strain is converted to calculate the stress at the reference strain rate, and is compared with the fracture limit line of the stress space corresponding to the reference strain rate.

FIG. 23 is a flowchart showing each step in the case where fracture prediction is performed in the process of forming a thin plate made of a metal material by the fracture prediction method according to this embodiment.
First, the material and mechanical characteristic values (t, YP, TS, El, U.El, r value,
Based on the n-th power hardening law / Swift hardening law), the estimating unit 1 estimates the fracture limit line of the strain space in the proportional load path (step S1).

  Subsequently, the conversion unit 2 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, and creates a stress FLD (step S2).

  Subsequently, the fracture determination unit 3 determines the strain state of each part obtained from the fracture limit line of the stress space converted by the conversion unit 1 and the simulation result of the plastic deformation process by the finite element method (here, the dynamic explicit method). Is evaluated by comparing the positional relationship with the above, and a breakage or its risk is judged (step S3).

In step S3, when it is determined that the critical strain has been reached and the thin plate is ruptured or has a high risk, the rupture determination unit 3 executes the following processing (step S4).
Outputs element ID, sheet thickness, strain, and stress information to a log file. Furthermore, the elements that have reached the criteria are deleted, and the analysis after the fracture is continued.

Subsequently, the following various displays are performed on the display unit 4 (step S5).
The risk of breakage of the thin plate is contoured with a scalar amount. In addition, the stress history and criteria of the fracture risk site in the stress space are displayed. At the same time, the risk of wrinkling in the thin plate is displayed in contour. Here, the risk of breakage may be displayed for the variation (average value, lower limit value) within the standard of the shipping test value.

  On the other hand, if it is determined in step S3 that there is no possibility of breakage or that the risk is low, this is displayed on the display unit 4 in step S6.

  FIG. 24 is a flowchart showing each step when the fracture prediction in the collision process is performed following the fracture prediction in the molding process of FIG. 23 by the fracture prediction method according to the present embodiment.

In this case, the stress FLD created in step S2 of FIG. 23 is taken over and used.
Then, the fracture determination unit 3 performs numerical analysis in consideration of the speed dependency of the deformation stress of the thin plate, converts the plastic strain obtained from the numerical analysis, calculates the stress at the reference strain rate, Compared with the fracture limit line of the stress space corresponding to the speed, the fracture or its risk is judged (step S11).

  In step S11, the fracture determination unit 3 takes over the deformation state of the thin plate evaluated by the numerical analysis in the forming process of FIG. 23 as the initial condition of the numerical analysis in the collision process. This deformation state is the thickness and equivalent plastic strain of the thin plate, or the plate thickness, equivalent plastic strain, stress tensor and strain tensor.

In Step S11, when it is determined that the thin plate is broken or the risk is high, the break determination unit 3 executes the following process (Step S12).
Outputs element ID, sheet thickness, strain, and stress information to a log file. Furthermore, the elements that have reached the criteria are deleted, and the analysis after the fracture is continued.

Subsequently, the following various displays are performed on the display unit 4 (step S13).
The risk of breakage of the thin plate is contoured with a scalar amount. In addition, the stress history and criteria of the fracture risk site in the stress space are displayed. At the same time, the risk of wrinkling in the thin plate is displayed in contour. Here, the risk of breakage may be displayed for the variation (average value, lower limit value) within the standard of the shipping test value.

  On the other hand, if it is determined in step S11 that there is no possibility that the thin plate will break or that the risk is low, this is displayed on the display unit 4 in step S14.

  As described above, according to this embodiment, 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 obtained with high prediction accuracy. Can be determined. This makes it possible to quantitatively evaluate the risk of press forming and breakage at the time of collision, and realizes efficient and highly accurate development of an automobile body that simultaneously considers materials, construction methods, and structures.

Example 4
The function of each component (except for the display unit 4) constituting the fracture prediction device according to the above-described embodiment can be realized by operating a program stored in a RAM or ROM of a computer. Similarly, each step (steps S1 to S6 in FIG. 23, steps S11 to S14 in FIG. 24, etc.) of the fracture prediction method 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. 25 is a schematic diagram illustrating an internal configuration of a personal user terminal device. In FIG. 25, reference numeral 1200 denotes a personal computer (PC) provided with 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 S6 in FIG. 23 of the embodiment, steps S11 to S14 in FIG. 24, and the like 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 figure which shows the shaping | molding limit diagram (FLD) used for description of the prior art. It is a shaping | molding limit diagram used for description of the subject which this invention tends to solve. It is a figure for demonstrating conversion from distortion to stress. It is a figure for demonstrating a coordinate transformation rule. It is a diagram showing that the fracture limit line of the stress space can be expressed by a single curve, while the FLD of the strain space changes greatly depending on the deformation path, and the fracture limit line of the stress space changes greatly. It is a figure which shows the relationship between shaping | molding height and the largest principal distortion. It is a figure which shows the comparison of the prediction precision when performing numerical simulation on various analysis conditions, and using FLD obtained from the experiment and the local constriction generation limit as a fracture criterion. It is a figure which shows the positional relationship of the stress log | history of a shaping | molding process obtained by numerical simulation, and a fracture | rupture limit line. It is a figure which shows the prediction precision of the method of this invention. It is a figure which shows the part of a hat cross-sectional shape which is a verification object of the prediction accuracy of a collision analysis, and a 3 point | piece bending drop test outline. It is a figure which shows the analysis result of the hat-shaped drawing bending molding by numerical simulation. It is a figure which shows the relationship of the equivalent stress according to equivalent plastic strain and strain rate. It is a figure which shows the positional relationship of the dynamic stress obtained from the dynamic breaking stress limit line in a stress space, and a collision simulation. It is a figure which shows the positional relationship of the stress log | history of a shaping | molding process obtained by numerical simulation, and a fracture | rupture limit line, and the prediction accuracy of this invention method. It is the figure used for description of the Example of this invention, and is the figure explaining the experiment method. It is a figure used for description of the Example of this invention, and is a figure explaining the analysis model. It is the figure used for description of the Example of this invention, and is the figure which displayed the analysis result with the contour with respect to the largest principal strain distribution. It is the figure used for description of the Example of this invention, and is the figure which showed the relationship between the distance from a hole edge, and the largest principal strain regarding an analysis result. It is the figure used for description of the Example of this invention, and is the figure which showed the relationship between the distance from a hole edge, and the largest principal strain regarding an analysis result. It is a figure used for description of the Example of this invention, and is a figure which shows the positional relationship of the stress log | history of the shaping | molding process obtained by numerical simulation, and a constriction generation | occurrence | production limit stress line. It is a figure used for explanation of an example of the present invention, and is a figure showing a positional relation of a fracture criterion obtained by converting a stress history of a forming process, a necking generation limit stress line, and a hole expansion rate into a stress space obtained by numerical simulation. It is. It is a block diagram which shows the main structures of the fracture prediction apparatus by a present Example. It is a flowchart which shows each step in the case of performing fracture | rupture prediction in the formation process of the thin plate which consists of metal materials with the fracture | rupture prediction method by a present Example. It is a flowchart which shows each step in the case of performing fracture | rupture prediction in a collision process following the fracture | rupture prediction in the shaping | molding process of FIG. 23 by the fracture | rupture prediction method by a present Example. It is a schematic diagram which shows the internal structure of a personal user terminal device.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Estimation part 2 Conversion part 3 Break determination part 4 Display part

Claims (27)

A fracture prediction method for evaluating the fracture limit of a thin plate made of a metal material,
In predicting the occurrence of breakage of the thin plate in the plastic deformation process in response to one or more deformation path changes,
A procedure for converting the fracture limit line of the strain space into the fracture limit line of the stress space;
And a procedure for predicting the presence or absence of the occurrence of the fracture using the obtained fracture limit line of the stress space. In the procedure for predicting the presence or absence of breakage,
The deformation state of the thin plate is evaluated by numerical analysis, the obtained strain is converted into stress, and the presence or absence of the breakage is quantitatively evaluated using the break limit line of the stress space. The fracture prediction method according to 1. In predicting the occurrence of breakage of the thin plate corresponding to each of the plurality of plastic deformation processes,
The deformation state of the thin plate evaluated by the numerical analysis in the plastic deformation process in the previous stage is inherited as an initial condition of the numerical analysis in the plastic deformation process in the subsequent stage. Fracture prediction method.   The fracture prediction method according to claim 3, wherein the deformation state of the thin plate is a plate thickness and equivalent plastic strain of the thin plate, or the plate thickness, equivalent plastic strain, stress tensor and strain tensor.   5. The fracture prediction method according to claim 3, wherein the plastic deformation process in the previous stage is a forming process of the thin plate, and the plastic deformation process in the subsequent stage is a collision process of the thin plate. In the procedure of converting to the fracture limit line of the stress space,
The fracture prediction method according to any one of claims 1 to 5, wherein the fracture limit line of the strain space is obtained from an experiment. In the procedure of converting to the fracture limit line of the stress space,
The fracture prediction method according to any one of claims 1 to 5, wherein the fracture limit line of the strain space is theoretically estimated from a mechanical characteristic value.   The fracture prediction method according to claim 7, wherein a constriction start line in the strain space is converted into the stress space, and a fracture limit line of the stress space is obtained. In the procedure for predicting the occurrence of breakage,
The strain obtained from the deformation state of the thin plate evaluated by an experiment is converted into stress, and the presence or absence of the breakage is quantitatively evaluated using a breakage limit line of the stress space. The fracture | rupture prediction method of description.   The fracture prediction method according to claim 2, wherein a finite element method is used as the numerical analysis method.   When using the dynamic explicit method that is one of the finite element methods as the numerical analysis method, the plastic strain obtained by the dynamic explicit method is converted into stress and compared with the fracture limit line of the stress space. The method for predicting fracture according to claim 10, wherein: In the procedure for predicting the occurrence of breakage,
The numerical analysis is performed in consideration of the speed dependency of the deformation stress of the thin plate, the plastic strain obtained from the numerical analysis is converted to calculate a stress at a reference strain rate, and the stress corresponding to the reference strain rate is calculated. The fracture prediction method according to claim 1, wherein the fracture prediction method is compared with a fracture limit line of a stress space.   The fracture prediction method according to any one of claims 1 to 12, wherein the thin plate is made of a high-strength material having a tensile strength of 440 MPa or higher.   The fracture according to any one of claims 1 to 6, and 9 to 13, wherein the fracture prediction of the material is determined using a criterion obtained by converting a hole expansion rate obtained from a hole expansion test into a stress space. Prediction method. A fracture prediction device for evaluating the fracture limit of a thin plate made of a metal material,
In predicting the fracture occurrence of the thin plate in the plastic deformation process according to one or more deformation path changes,
A conversion means for converting the fracture limit line of the strain space into the fracture limit line of the stress space;
And a predicting means for predicting the presence or absence of the occurrence of the fracture using the obtained fracture limit line of the stress space.   The predicting means evaluates the deformation state of the thin plate by numerical analysis, converts the obtained strain into stress, and quantitatively evaluates the presence or absence of the breakage using the break limit line of the stress space. The fracture prediction device according to claim 15, wherein the device is a fracture prediction device.   The fracture prediction apparatus according to claim 15 or 16, wherein the fracture limit line of the strain space is obtained from an experiment.   The fracture prediction apparatus according to any one of claims 15 to 17, further comprising estimation means for theoretically estimating the fracture limit line of the strain space from a mechanical characteristic value.   19. The fracture prediction apparatus according to claim 18, wherein the conversion means converts a constriction start line in the strain space into the stress space and acquires a fracture limit line of the stress space.   The predicting means converts the strain obtained from the deformation state of the thin plate evaluated by experiment into stress, and quantitatively evaluates the presence or absence of the rupture using the rupture limit line of the stress space. The fracture prediction device according to claim 15.   The fracture prediction apparatus according to any one of claims 16 to 19, wherein the prediction means uses a finite element method as the numerical analysis method.   When the dynamic explicit method that is one of the finite element methods is used as the numerical analysis method, the predicting means converts the plastic strain obtained by the dynamic explicit method into stress, and the fracture limit line of the stress space The fracture prediction device according to claim 21, wherein   The predicting means performs the numerical analysis in consideration of the speed dependence of the deformation stress of the thin plate, converts the plastic strain obtained from the numerical analysis to calculate a stress at a reference strain rate, and calculates the reference strain The fracture prediction device according to any one of claims 15 to 19, wherein the fracture prediction device is compared with a fracture limit line of the stress space corresponding to a speed.   The fracture prediction apparatus according to any one of claims 15 to 23, wherein the thin plate is made of a high-strength material having a tensile strength of 440 MPa or higher.   25. The fracture according to any one of claims 15, 16, and 20 to 24, wherein the fracture prediction of a material is determined using a criterion obtained by converting a hole expansion rate obtained from a hole expansion test into a stress space. Prediction device.   The program which makes a computer perform each procedure of the fracture | rupture prediction method of any one of Claims 1-14.   A computer-readable recording medium on which the program according to claim 26 is recorded.

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