JP2008119739A - Method for quantitatively judging risk of rupture of worked article and die designing method using the same method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To make the quantitative judgement of the risk of rupture possible on the basis ob a numerical value by determining the degree of the risk of the rupture as the numerical value of a concrete value. <P>SOLUTION: In this method, the degree of the risk of the rupture which occurs on a worked article in a press working simulation of a material to be worked using a computer is determined by the concrete numerical value on the basis of a numerical formula by determining the numerical formula by which the degree of the risk of the rupture can be shown as the numerical value of the concrete value by grasping the numerical formula showing the existence (conditions) of the occurrence of the rupture presented by the theory of three-dimension local bifurcation from the viewpoint like the theory of instability and the design work of the die and the correcting work of the die using the method are performed. Since the degree of the risk of the rupture is obtained as the concrete numerical value in this invention, the judgement is accurately performed and the design work of the die and the correcting work of the die are correctly performed. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a technology for quantitatively determining the risk of breakage occurring in a work material by specific numerical values in press work simulation of a work material (metal plate material) using a computer, and press work using this method. This is a technique related to mold design work and mold correction work to avoid the occurrence of breakage in the material.

Avoiding breakage in press working is an important requirement.
Therefore, if it is found that the actual product will be crushed and the workpiece will break as a result, it will usually take time and cost loss to modify the mold to avoid breakage. A press working simulation using a metal mold was performed to predict the occurrence of breakage.

  Conventionally, using the strain representing the degree of deformation of the workpiece obtained from the press working simulation, the fracture limit of the plate deformation plotted on the plane defined by the maximum and minimum strain directions in the plate surface of the workpiece. The presence or absence of breakage was determined by a diagram (hereinafter referred to as a “strain limit diagram due to strain”).

  However, in the determination using the forming limit diagram based on the strain, only the presence or absence of breakage can be determined, and the degree of risk of breakage, clogging, and quantitative information on breakage cannot be obtained.

  In addition, since the strain limit diagram due to strain was prepared based on the test piece test results in advance or based on the theoretical formula, the applicable range was limited and the strain was limited. Even if the values are the same, if the process leading to the strain is different, the determination of the presence or absence of fracture changes, so-called strain path dependency.

  For this reason, when it is actually pressed based on the forming limit diagram due to strain, it does not break even if it is deformed (predicted to break) beyond the forming limit point (line) in the drawing, and conversely, Since there is a case where it breaks even if it is deformed just before the part (predicted not to break), there is uncertainty in the judgment of breakage based on the figure, and the final judgment is an expert It was done with experience and intuition.

ここで、
σは、破断発生時の応力テンソル
ｎは、分岐界面の法線ベクトル
ｍは、分岐界面に平行で且つ破断発生の方向のベクトル
Ｑは、変数に上記σとｎとを用いた数式
ｍｉｎ［］は、［］で表される数式の最小値である。
以下、上記数式を「数式１」という。
展開発展させて破断発生の有無（条件）を、破断発生時の応力の大きさと加工硬化率との比によって一意に表せる下記数式を求め、

ここで、
σは、破断発生時の応力の大きさ
ｈは、加工材の加工硬化率
ｎは、分岐界面の法線ベクトル
ｍは、分岐界面に平行で且つ破断発生の方向のベクトル
ｓは、応力の方向を表す単位テンソル
ＨとΣは、変数に上記ｍ、ｎを用い、パラメータにｓが与えられる数式
ｍｉｎ()は、括弧内の最小値
（）ｃｒは、括弧内によって定義される局所変形の条件である。
以後、上記数式を「数式２」という。 Therefore, the inventor of the present application represents the presence or absence (condition) of the occurrence of breakage, which is presented in the three-dimensional local branching theory, in order to solve the above-mentioned drawbacks before this application (breakage occurs when the minimum value becomes 0). To the following formula:

here,
σ is the stress tensor n at the time of fracture occurrence, the normal vector m of the branch interface is parallel to the branch interface, and the vector Q in the direction of fracture occurrence is the formula min [] using the above σ and n as variables. Is the minimum value of the mathematical expression represented by [].
Hereinafter, the above formula is referred to as “Formula 1”.
Develop and develop the following formula that can uniquely represent the presence or absence (conditions) of fracture occurrence by the ratio of the magnitude of stress at the time of fracture occurrence and the work hardening rate,

here,
σ is the magnitude of stress at the time of fracture occurrence h is the work hardening rate n of the workpiece, the normal vector m of the branch interface is parallel to the branch interface, and the vector s in the direction of fracture occurrence is the direction of the stress The unit tensors H and Σ, which represent the above, use m and n as variables and s is given as a parameter. The formula min () is the minimum value in parentheses () cr is the local deformation condition defined by the parentheses. It is.
Hereinafter, the above formula is referred to as “Formula 2”.

Based on the formula, or a method for determining breakage occurring in a workpiece based on a molding limit diagram of a workpiece created based on the formula, and further, the deformation of the molding limit diagram may be broken The timing of shifting to a state where there is a possibility of fracture due to the occurrence of local deformation in which a part of the plate thickness decreases from the undeformed deformation (hereinafter referred to as “lower limit of fracture”), and further, the local where the plate thickness decreases Plotting both values in the same coordinate system together with the timing (hereinafter referred to as the "upper limit of fracture") that ultimately leads to fracture due to the occurrence of local deformation that penetrates the plate thickness inside the deformation, Forming limit in which the vertical axis shows the ratio σ1 / h of the maximum stress magnitude σ1 and the work hardening rate h, and the horizontal axis plots the ratio σ2 / h of the minimum stress magnitude σ2 and the work hardening rate h Using a diagram (see FIG. 1, A is the lower limit of breakage, B is the upper limit of breakage) It proposed a solution for determining the method of fracture of the workpiece, characterized in that, filed them.
For details, refer to Patent Document 1 described at the end of the application.

  However, in the above-described method using FIG. 1, Equation 2 can only determine the presence or absence of breakage, so that after the plotted value exceeds the lower limit of breakage (A), it approaches the upper limit of breakage (B). Although it can be intuitively understood that the risk increases, the degree of the risk of fracture cannot be determined by a specific numerical value.

  An object of the present invention is to obtain the degree of risk of fracture described above as a specific numerical value and to quantitatively determine the risk of fracture based on the numerical value.

  Furthermore, this method is used for press work mold design work and mold correction work to accurately avoid breakage occurring in the work material.

ここで、
Ｉは、破断の危険性の程度を表わす不安定指数
σは、破断発生時の応力テンソル
ｎは、分岐界面の法線ベクトル
ｍは、分岐界面に平行で且つ破断発生の方向のベクトル
ｓは、応力の方向を表す単位テンソル
Ｗｄは、要求仕事率、即ち、破断発生に必要なエネルギーの変化率
Ｗｓは、供給仕事率、即ち、加工材に作用する応力が破断発生に影響を与えるエネルギーの変化率
である。
以後、上記数式を「数式３」という。 In the present invention, in order to obtain the degree of risk of fracture described above as a specific numerical value, in the above-mentioned application, Formula 1 to Formula representing presence / absence (condition) of occurrence of fracture presented in the three-dimensional local branch theory Instead of obtaining 2, the above-described mathematical formula 1 is grasped from the viewpoint of instability and the following mathematical formula is obtained.
For the relationship between the three-dimensional local bifurcation theory and the instability theory, refer to non-patent document 3 at the end.

here,
I is the instability index σ representing the degree of risk of fracture, the stress tensor n at the time of fracture occurrence, the normal vector m of the branch interface, the vector s parallel to the branch interface and the direction of fracture occurrence is The unit tensor Wd representing the direction of stress is the required work rate, that is, the change rate Ws of energy required for occurrence of breakage, and the supply work rate, that is, the change in energy that the stress acting on the workpiece affects the occurrence of breakage. Rate.
Hereinafter, the above formula is referred to as “Formula 3”.

  And since I (unstable index) in Equation 3 indicates the degree of risk of breakage as a specific value, based on this, it can be used as a processed product in a press working simulation of a workpiece using a computer. This is a method of determining the degree of risk of breakage occurring by specific numerical values, and a method of performing mold design work and mold correction work using the method.

  Since the present invention can thus obtain the degree of risk of fracture as a specific numerical value, for example, the degree of risk of fracture in the region between AB in FIG. 1 can be accurately determined.

  In addition, if this is used for the mold design work and the mold correction work in the press work simulation of the work material using a computer, the degree of risk of breakage in the initially designed mold is considered by considering the numerical value. If there is a large part, disperse the force acting on the part to another part where the risk of breakage is small, or appropriate so that a part with a high risk of breakage does not occur newly It is possible to select an appropriate dispersion point and to make an optimal balance between the degree of risk of breakage of the entire mold.

  In order to solve the above-mentioned problem, the present invention replaces the invention previously filed by the applicant of the present application, that is, Equations 1 to 2 representing the presence or absence (condition) of occurrence of breakage presented in the three-dimensional local branch theory. Instead of obtaining, Equation 1 is obtained from the viewpoint of instability, and Equation 3 is obtained, and further, I (unstable index) of Equation 3 indicates the degree of risk of fracture as a specific numerical value. Based on this, based on this, the degree of risk of breakage occurring in the processed product in the press processing simulation of the workpiece using a computer is determined by specific numerical values, and the mold design using it It is characterized in that the work and the mold correction work are performed.

  In the three-dimensional local bifurcation theory, the occurrence of rupture is regarded as a bifurcation phenomenon that suddenly switches from a state of uniform deformation until then to a local deformation in which only one part is deformed and the other does not spread. The determination of breakage is performed based on a mathematical expression relating to the condition under which this occurs.

  Then, the breaking condition is expressed by the above-described Expression 1, and it is argued that the breaking occurs when the minimum value of the Expression 1 becomes 0, that is, the condition for the breaking is satisfied.

ここで
σは、破断発生時の応力テンソル
ｎは、分岐界面の法線ベクトル
ｍは、分岐界面に平行で且つ破断発生の方向のベクトル
Ｑは、変数に上記σとｎとを用いた数式である。
以下、上記数式を「数式４」という。 Hereinafter, the process of obtaining Formula 3 by expanding Formula 1 will be described in detail.
By the way, when Expression 1 is expressed from a general viewpoint that is not limited to the minimum value, the following Expression is obtained.

Here, σ is the stress tensor n at the time of break occurrence, the normal vector m of the branch interface is parallel to the branch interface, and the vector Q in the direction of break occurrence is an equation using the above σ and n as variables. is there.
Hereinafter, the above formula is referred to as “Formula 4”.

By the way, as described in the section of the background art, Formula 1 can be expressed by Formula 2 using Formula H [m, n: s] related to σ and Formula Σ [m, n: s] related to h.
For details of the process of expanding Formula 1 and obtaining Formula 2, refer to Patent Document 4 described at the end.

σ（太文字）は、破断発生時の応力テンソル
σ（細文字）は、破断発生時の応力の大きさ
ｈは、加工材の加工硬化率
ｎは、分岐界面の法線ベクトル
ｍは、分岐界面を挟んだ両端が移動する方向のベクトル
ｓは、応力の方向を表す単位テンソル
ＨとΣは、変数に上記ｍ、ｎを用い、パラメータにｓが与えられる数式である。
以下，上記数式を数式５という。 Then, the mathematical formula 4 can also be expressed by the following mathematical formula using the mathematical formula H [m, n: s] related to σ and the mathematical formula Σ [m, n: s] related to h.

σ (bold character) is the stress tensor at the time of rupture σ (thin character) is the magnitude of the stress at the time of rupture h, the work hardening rate n of the workpiece, the normal vector m of the branch interface is the branch The vector s in the direction in which both ends of the interface move is the unit tensors H and Σ representing the direction of stress, and is a mathematical formula in which m and n are used as variables and s is given as a parameter.
Hereinafter, the above formula is referred to as Formula 5.

  In the three-dimensional local branch theory, the moment when the left-side value of Equation 1 is 0 is defined as a break, so the moment when the left-side value of Equation 5 obtained by developing from Equation 1 is 0 can be defined as a break. .

Here, when Equation 5 is taken from an anxiety point of view and expressed in the form of a stability criterion equation, Equation 3 described above is obtained.
For details of the three-dimensional local branching theory, refer to Chapter 9, page 215 of Non-Patent Document 1 described at the end.

The reason for this is that the branching criterion and the stability criterion coincide with each other with respect to the breakage of the workpiece. Therefore, a mathematical expression representing the branching condition (Formula 5) and a mathematical expression representing the stability criterion, that is, the unstable condition (Formula 3). Is the same.
For details, refer to the non-patent document 3 at the end.

And, the process of breakage of the workpiece described in the three-dimensional local branch theory (specifically, the process from the lower limit A of fracture to the upper limit B of fracture in FIG. 1) is interpreted from an unstable viewpoint,
Before and after the lower limit of fracture A More specifically, the process in which the deformation of the work material undergoes “local deformation” in which a part of the plate thickness decreases from “uniform deformation” where there is no possibility of fracture is It can be interpreted as a process from a stable equilibrium state where “uniform deformation” does not change to an unstable equilibrium state where “uniform deformation” behind A changes to “local deformation”.
Before and after the upper limit B of breakage Specifically, the progress of “local deformation” of the workpiece and “breakage” occurs from a stable equilibrium state that does not change in terms of “local deformation” before B. , B can be interpreted as a process leading to an unstable equilibrium state changing from “local deformation” behind “B” to “breaking”.

Therefore, considering the point obtained by taking Equation 3 from the viewpoint of instability, and considering in accordance with the occurrence of breakage in the above item (2) of the progress of breakage of the work material in press working,
Wd is the rate of change of energy required to change from “local deformation” to “breakage occurrence” (hereinafter referred to as “rate of change of energy necessary for breakage occurrence” or “required power”). ) And
Ws is the rate of change in energy at which the stress acting on the workpiece affects the occurrence of fracture because it changes from “local deformation” to “break occurrence” (hereinafter referred to as “the stress acting on the workpiece breaks. The rate of change in energy that affects the “power supply rate” or “supply power”), and I represents the stability of the equilibrium state.

By the way, instability theory, the stability of the equilibrium state is defined as “the ability of a particular equilibrium state to withstand and maintain various disturbances”. In other words, it means a high quantitative ability to maintain an equilibrium state.
Therefore, since I means a margin until the occurrence of breakage, it can be said that the index represents the degree of risk of breakage (hereinafter referred to as “unstable index”).
Then, the value of the instability index I can be quantitatively obtained as a specific numerical value by the mathematical formula 3, and this point is a feature of the present invention.

Then, if this Equation 3 is considered in accordance with before and after the occurrence of breakage of the workpiece in press working, the branch point at which Wd = Ws (I = 0) changes from “local deformation” to “breakage”. is there.
As a result, the value of I (unstable index) represented by the difference between the supply power (Ws) and the required power (Wd) is clogged with a margin (stability in the equilibrium state) until breakage occurs. The degree of the possibility of occurrence ”, and this value can be obtained as a specific numerical value.
As described at the end of the above [Background Art] section, it has been conventionally known that the area between the lower limit of fracture and the upper limit of fracture is a risk area of fracture occurrence. It was not possible to quantitatively calculate the "degree of possibility" as a specific numerical value.
However, since the present invention can quantitatively determine the “degree of possibility of breakage” of the region as a specific numerical value using the instability index, until the upper limit of breakage or the lower limit of breakage is reached. It is possible to grasp how much room is left.

  FIG. 2 is a graph showing the result of calculating the value (C) of the instability index in a region between the lower limit (A) of fracture and the upper limit (B) of fracture according to a specific example (the vertical axis represents the instability index). I, the horizontal axis is the ratio σ / h) between the magnitude of stress at the time of fracture occurrence and the work hardening rate.

The present invention can accurately grasp the degree (situation) of the risk of rupture of the entire work piece by using the graph. For example, the design work of the mold in the press work simulation of the work material using a computer, In the mold correction work,
[Region between AB]
If there is a location where the risk of fracture occurrence is large (location where the value of I is close to 0) in the region, the force acting on the location may be distributed to another location where the risk of fracture occurrence is small In that case, it becomes possible to select an appropriate dispersive part so that a part with a high risk of breakage does not occur newly,
[Region beyond B]
In this region, the breakage occurs surely, but considering the value of I, it becomes a measure of how much correction (repair) is necessary to eliminate the breakage.
[Regarding the area in front of A]
In this region, the value of I in the region between AB almost always increases exponentially along the A line, so there is little need to consider, but depending on the value of I in this region A safer (optimally balanced) mold design is possible.

The above-mentioned instability index is a value obtained for one point in the thickness direction.
However, considering the fact that the workpiece that is the object of press forming is a thin plate but has a finite thickness, different stresses act on the plate surface and inside the plate, making it unstable in the plate thickness direction. You can imagine that the index is a different value.
Therefore, by integrating the instability index in the plate thickness direction, it is possible to accurately determine the “degree of risk of occurrence of fracture” for the entire cross section in the plate thickness direction of the workpiece, and the integrated value is the plate thickness of the workpiece. It can also be used for mold design work and mold correction work in the direction.

Edited by Japan Society for Technology of Plasticity, published by Corona on July 7, 2004 "Static Solution FEM-Plate Molding" Akiyoshi Sugano, Satoshi Nitta, Junichi Ito, Yoshihiro Kamada, Taketoshi Sagawa, Japan Society for Technology of Plasticity 2001, “Plasticity and Processing” (periodical publication) Vol. 42, No. 489, pages 1076-1079 Band branching analysis method and results with single particles (ductile fracture of FCC crystals due to shear band formation 1st report) " Ito Junichi, Japan Society for Technology of Plasticity, published in 1998, “Plastics and Processing” (Regular Publication) Vol. 39, No. 444, pp. 24-28 “Plastic Instability / Branching Phenomena in Sheet Forming” Japanese Patent Application No. 2006-289605

Forming limit diagram of workpiece based on σ / h Graph showing changes in instability index

Claims (5)

  In the press working simulation of a workpiece using a computer, the required power, that is, the rate of change of energy necessary for occurrence of breakage, and the supply power, that is, the energy that affects the occurrence of breakage of the stress acting on the workpiece. A method for quantitatively determining the risk of breakage, characterized in that the degree of risk of breakage occurring in a processed product is determined by a specific numerical value based on an instability index expressed by a difference from a change rate. A method for quantitatively determining the risk of fracture, wherein the instability index according to claim 1 is obtained by the following equation.

here,
I is the instability index σ representing the degree of risk of fracture, the stress tensor n at the time of fracture occurrence, the normal vector m of the branch interface, the vector s parallel to the branch interface and the direction of fracture occurrence is The unit tensor Wd representing the direction of stress is the required work rate, that is, the change rate Ws of energy required for occurrence of breakage, and the supply work rate, that is, the change in energy that the stress acting on the workpiece affects the occurrence of breakage. Rate. The instability index according to claim 1 is obtained in the plate thickness direction of the workpiece, and by integrating these, the risk of breakage regarding the entire cross section in the plate thickness direction of the workpiece is determined by a specific numerical value. Quantitative determination method of the risk of breaking as a feature. The instability index (I) according to claim 2 is set on the vertical axis, and the ratio (σ / h) between the magnitude (σ) of the stress acting on the workpiece and the work hardening rate (h) is set on the horizontal axis. Breakage occurring in a workpiece using a graph in which a line (A) representing the lower limit of breakage, a line (B) representing the upper limit of breakage, and the value of the instability index (I) are plotted in the coordinate system A method for quantitatively determining the risk of breakage, characterized in that the degree of risk is determined. Using the quantitative determination method of the risk of fracture according to any one of claims 1 to 4, performing a mold design work or a mold correction work in a press working simulation of a workpiece. Mold design method.

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