JP7206902B2 - Formability evaluation method, program and recording medium - Google Patents

Description

The present invention relates to a moldability evaluation method, a program, and a recording medium.

In recent years, the application of high-strength steel sheets to automobile bodies is rapidly progressing due to the demand for collision safety and weight reduction. These high-strength steel sheets can increase the absorption energy and strength at the time of collision without increasing the plate thickness. However, the decrease in ductility associated with the increase in strength of steel sheets increases the risk of fracture during press forming.

The margin for breakage during forming is generally determined using the plate thickness reduction rate and forming limit diagram (FLD). FLD is a diagram showing the maximum principal strain that gives the fracture limit for each minimum principal strain, and is used for fracture evaluation in forming analysis and collision analysis. In general, the method of measuring FLD by experiment is to draw a circle-shaped or lattice-shaped pattern on the surface of a metal plate in advance by etching or the like, break it by hydraulic forming or stretch forming with a rigid tool, and then measure the deformation of the circle. Measure the critical strain at break from the volume. The rupture limit line is obtained by proportionally loading the metal plate for various in-plane strain ratios, plotting the rupture limit strains at each strain ratio on the principal strain axis and connecting them with a line (Fig. 1).

On the other hand, as theoretical prediction of FLD, there are various methods such as combination of Hill's local constriction model and Swift's diffusion constriction model, Marciniak-Kuczynski method, and Storen-Rice model. Ductile fracture of materials occurs at the location where the deformation is localized due to local constriction. When this local constriction occurs, it leads to fracture in an extremely short time. Therefore, in practice, the fracture limit is often considered to be the local constriction generation limit, and the fracture limit prediction is often handled within the framework of plastic instability. By comparing the positional relationship between the rupture limit line obtained in this way and the strain state of each part obtained from the results of numerical simulation using the finite element method, the risk of rupture is evaluated. When the strain is reached, it is judged that the breakage or the risk of breakage is high.

JP 2011-140046 A JP 2012-170993 A

Hill, R.: J. Mech. Phys. Solids, 4 (1956) 247

FLD obtained from experiments and theoretical predictions is targeted when the material separates under uniform stress conditions or when local constriction occurs (Fig. 2). However, in stretch flanging, where cracks form at the edge of the steel sheet, strain decreases inward from the edge of the flange, so the edge of the material is restrained from the inside and the occurrence of constriction is suppressed (Fig. 3). . That is, even if the stretch flange edge satisfies the fracture condition in a uniform distribution, the condition has not yet been reached on the inside, so the support effect on the inside cannot lead to a plastically unstable state as a whole and does not lead to fracture. . This point is different from local constriction generation in a uniform stress field such as uniaxial tension, bulging, and deep drawing. The conditions for the occurrence of plastic instability have not yet been elucidated.

The present invention quantitatively evaluates the risk of fracture of a stretch flange portion having a strain gradient from the plate edge toward the inside, and avoids the stretch flange fracture, which is a forming problem in high-strength steel sheets, to achieve high It is an object of the present invention to provide a formability evaluation method, a program, and a recording medium capable of realizing press forming of strong and lightweight parts.

In order to solve the above problems, the present inventors have made intensive studies and conceived the following aspects of the invention. The gist of the present invention is as follows.

1. For the thin plate to be tested, from the relationship between the stress and strain obtained by the tensile test ,
In the hole expansion test , D0 is the diameter of the cylindrical punch, _d0 is the initial diameter of the hole in the thin plate, _d is the diameter of the hole in the deformation process of the thin plate, t is the thickness of the thin plate, and t is the thickness of the thin plate. When the circumferential stress in the radial direction from the edge is σ _θ , the work hardening rate is dσ _θ /dε _θ , and the radial coordinate is r,

Calculate the value of d that satisfies the rupture limit hole expansion rate

a first step of theoretically calculating
A second step of calculating the fracture limit strain of the plate end based on the fracture limit hole expansion ratio calculated in the first step;
a third step of evaluating that the risk of fracture is high when the maximum principal strain obtained from numerical analysis by the finite element method reaches the fracture limit strain calculated in the second step;
including
A formability evaluation characterized in that the first step, the second step, and the third step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. Method.

2 . 1. The method is characterized in that the circumferential stress in the radial direction from the edge of the hole in the thin plate is obtained by numerical analysis using the finite element method. The moldability evaluation method described in .

3 . 1. The strain distribution in the radial direction and the circumferential direction of the thin plate is obtained by numerical analysis using the finite element method for the circumferential stress in the radial direction from the hole edge of the thin plate, and the strain distribution is used to obtain the strain distribution. The moldability evaluation method described in .

4 . 1. The strain distribution of the thin plate is determined by experiments, and the circumferential stress in the radial direction from the hole edge of the thin plate is determined using the strain distribution. The moldability evaluation method described in .

5 . 1. The strain distribution of the thin plate is obtained by series expansion or linear approximation of the circumferential stress in the radial direction from the hole edge of the thin plate, and the strain distribution is used to obtain the strain distribution. The moldability evaluation method described in .

6 . further comprising, prior to the first step, a fourth step of calculating damage to the punch due to shearing;
The first step, the second step, the third step, and the fourth step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. 1. ~ 5 . Moldability evaluation method according to any one of.

7 . In the fourth step, the hardness of the sheared edge is used to calculate the plastic strain ε _θ introduced to the sheared edge of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate. 6. Do. The moldability evaluation method described in .

8 . In the fourth step, the relationship between the ratio _d0 /t of the initial hole diameter _d0 of the thin plate and the thickness _t of the thin plate, the ductility et of the thin plate, and the clearance c between the punch and the die during shearing. is used to calculate the plastic strain ε _θ introduced to the sheared end face of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate.6 . The moldability evaluation method described in .

9 . In the fourth step, the plastic strain ε _θ introduced to the sheared end surface of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated by shear simulation by the finite element method. 6. Do. The moldability evaluation method described in .

10 . For the thin plate to be tested, from the relationship between the stress and strain obtained by the tensile test ,
In the hole expansion test , D0 is the diameter of the cylindrical punch, _d0 is the initial diameter of the hole in the thin plate, _d is the diameter of the hole in the deformation process of the thin plate, t is the thickness of the thin plate, and t is the thickness of the thin plate. When the circumferential stress in the radial direction from the edge is σ _θ , the work hardening rate is dσ _θ /dε _θ , and the radial coordinate is r,

Calculate the value of d that satisfies the rupture limit hole expansion rate

a first step of theoretically calculating
A second step of calculating the fracture limit strain of the plate end based on the fracture limit hole expansion ratio calculated in the first step;
a third step of evaluating that the risk of fracture is high when the maximum principal strain obtained from numerical analysis by the finite element method reaches the fracture limit strain calculated in the second step;
on the computer, and
A formability evaluation characterized in that the first step, the second step, and the third step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. program.

1 1 . 10. It is characterized in that the circumferential stress in the radial direction from the hole edge of the thin plate is obtained by numerical analysis using the finite element method. The moldability evaluation program described in .

1 2 . 10. Circumferential stress in the radial direction from the hole edge of the thin plate is obtained by numerical analysis using the finite element method to obtain strain distributions in the radial direction and the circumferential direction of the thin plate, and the strain distribution is used to obtain the strain distribution. The moldability evaluation program described in .

1 3 . 10. The strain distribution of the thin plate is obtained by experiments, and the circumferential stress in the radial direction from the hole edge of the thin plate is obtained using the strain distribution. The moldability evaluation program described in .

14 . 1 0 . The moldability evaluation program described in .

15 . further comprising, prior to the first step, a fourth step of calculating damage to the punch due to shearing;
The first step, the second step, the third step, and the fourth step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. 1 0 . ~ 1 4 . Moldability evaluation program according to any one of.

16 . In the fourth step, the hardness of the sheared edge is used to calculate the plastic strain ε _θ introduced to the sheared edge of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate. 1 5 . The moldability evaluation program described in .

17 . In the fourth step, the relationship between the ratio _d0 /t of the initial hole diameter _d0 of the thin plate and the thickness _t of the thin plate, the ductility et of the thin plate, and the clearance c between the punch and the die during shearing. is used to calculate the plastic strain ε _θ introduced to the sheared edge of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate 15 . The moldability evaluation program described in .

18 . In the fourth step, the plastic strain ε _θ introduced to the sheared end surface of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated by shear simulation by the finite element method. 1 5 . The moldability evaluation program described in .

19 . 10 . ~ 18 . A computer-readable recording medium characterized by recording the moldability evaluation program according to any one of .

According to the present invention, it is possible to theoretically calculate the fracture limit hole expansion ratio obtained in the cylindrical hole expansion test from the stress-strain relationship obtained from the tensile test, and apply this to the forming simulation to stretch flange The risk of breakage can be quantitatively evaluated. As a result, it is possible to avoid stretch flange fracture, which is a forming problem in high-strength steel sheets, and to realize press forming of high-strength and lightweight parts.

FIG. 2 is a forming limit diagram (FLD) used for explaining the conventional technology; FIG. 4 is a schematic diagram for explaining a local constriction in a uniform stress state; FIG. 4 is a schematic diagram for explaining a strain gradient directed inward from a plate edge of a stretch flange portion. It is a schematic diagram for demonstrating a cylindrical hole expansion test. 4 is a schematic diagram for explaining conditions of a cylindrical hole expanding test used in Example 1. FIG. 1 is a diagram for calculating a work hardening state from the hardness of a sheared end surface in Example 1. FIG. 1 is a characteristic diagram showing the relationship between a shearing factor and a work hardening state in Example 1. FIG. 1 is a schematic diagram of a work hardening state of a sheared end surface calculated by a shearing simulation in Example 1. FIG. It is a characteristic diagram showing the calculation result of the circumferential strain distribution in the radial direction from the hole edge in the cylindrical hole expansion test. FIG. 4 is a characteristic diagram for calculating a plastic instability index; FIG. 5 is a characteristic diagram for explaining the relationship between the plastic instability index and the stroke; 2 is a flowchart showing a method for evaluating formability in Example 2. FIG. It is a schematic diagram which shows an example which carried out moldability evaluation. FIG. 10 is a schematic diagram showing an example of moldability evaluation in Example 3. FIG. 2 is a schematic diagram showing the internal configuration of a personal user terminal device; FIG.

[Basic idea of moldability evaluation method]
In the following, when the stress of the thin plate to be tested is σ _ij and the _strain is _{ε ij , σ ij} and ε _ij are denoted by a dot. Similarly, when the strain in the circumferential direction is ε _θ , the strain in the radial direction is ε _r , and the strain in the plate thickness direction is ε _t , the stress rate dε _θ /dt obtained by differentiating ε _θ with respect to time and ε _r is obtained from differentiating with time The stress rate dε _r /dt and the strain rate dε _t /dt obtained by differentiating ε _t with respect to time are denoted by dots on ε _θ , ε _r , and ε _t .

At stress σ _ij , strain ε _ij , stress rate dσ _ij /dt and strain rate dε _ij /dt of the sheet under test, after time δh,

increment of Here, when δσ _ij and δε _ij are not uniquely determined, the following equation holds if the difference between the corresponding amounts in any two solutions is indicated with Δ (see Non-Patent Document 1).

To treat equation (1) under arbitrary boundary conditions, integrating the above equation over the volume V of the object yields the following equation.

Combining equation (2) and the principle of virtual work, the condition for determining the unique solution of δσ _ij and δε _ij can be expressed by the following equation.

where Δν _i represents the velocity difference in two or more possible deformation modes.

Next, consider the case where Equation (3) is applied to the axisymmetric deformation mode of a thin plate. Assuming the balance formula of the minute element and the law of constant volume, the radial coordinate r, the plate thickness t, the circumferential strain rate dε _θ /dt, the circumferential stress σ _θ , the radial strain rate dε _r /dt, the radial direction Using the stress σ _r and the strain rate dε _t /dt in the plate thickness direction, equation (3) is given by the following equation.

The present inventor applied the formula (4) to the hole expansion test and came up with a method of theoretically estimating the limit hole expansion ratio at which fracture occurs. The present invention will be described in detail below.
In the hole expansion test, a circular hole with a diameter of d ₀ is made in the material, the hole is expanded with a cylindrical punch with a diameter of D ₀ , and the breaking limit is when a crack occurs at the edge of the hole, and the diameter d at that time and the initial From the hole diameter d ₀ , the hole expansion ratio λ is obtained (Fig. 4).
λ=[(dd ₀ )/d ₀ ]×100

In the hole expansion test, stress and strain decrease from the edge of the hole toward the inside. In such a non-uniform deformation state, as can be seen from Eq. It is necessary to consider the stability condition. Von Mises yield condition, isotropic hardening law, total strain theory, and n-th power hardening law for work hardening of materials

, the plastic instability condition is given by the following equation from equation (4).

Here, when I indicates a positive value, only one solution is determined, and conversely, when I indicates a negative value, it is in a plastically unstable state. That is, it can be considered that the condition of plastic instability in which cracks occur at the edge of the hole is 0 in Equation (5). Therefore, if the formula (5) is calculated every moment in the deformation process of hole expansion and the value of d (the diameter of the hole after deformation) is determined so that the formula (5) becomes 0, it is the hole edge It is the diameter of the hole when cracking occurs.

Since the hole expansion test is performed as a post-punching forming, the forming limit is strongly affected by the damage introduced into the post-punching sheared edge. In the actual production site, the board edge remains sheared and the forming limit may be lowered compared to the cutting edge. By considering the effect of work hardening on the end face introduced during shearing, the forming limit of hole expansion can be predicted with high accuracy.

The work hardening state of the sheared edge can be estimated by actually measuring the hardness of the edge and referring to the relationship of material hardness Hv-equivalent plastic strain ε _eq -equivalent stress σ _eq . First, the end face of the punched end face is cut out and the hardness Hv of the cross section is measured. Next, in order to estimate the plastic strain from the hardness of the end face, the relationship between plastic strain ε _eq and Vickers hardness Hv is obtained by a tensile test, and this is
Hv = _KHV ( _εHV + _εeq ) ⁿ
is approximated by Furthermore, a tensile test _{revealed the relationship σ eq =} K (ε ₀ + _{ε eq )} ⁿ
get where K _HV , K, ε ₀ , n are material parameters. As described above, the equivalent plastic strain ε _eq and the equivalent stress σ _eq introduced during shearing can be estimated using the cross-sectional hardness Hv of the sheared end face.

Furthermore, using a method of estimating the work hardening state during shearing from the cross-sectional hardness, various steel sheets were subjected to shearing experiments to determine the ratio _d0 /t of the punched hole diameter _d0 and the plate thickness t of the material. , ductility e _t of the material, clearance c between the punch and the die during shearing, and other material/processing factors and the work hardening state. In addition to the experiments, the equivalent plastic strain ε _eq and the equivalent stress σ _eq can also be obtained by shear simulation using the finite element method, for example.

[Example]
Specific examples of the present invention will be described below.

(Example 1)
Hereinafter, a method for calculating the fracture limit hole expansion ratio will be described by taking a high-strength steel sheet of 1.6 mm thickness and 590 MPa class as an example. Here, for example, a cylindrical punch with a punch shoulder radius of 10 mm and a diameter of 90 mm and a cylindrical die with a die shoulder radius of 3 mm and a diameter of 96 mm are used to punch a 10 mm diameter hole in the center of a 150 mm diameter blank. (Fig. 5).

The work-hardened state of the sheared end face is estimated by actually measuring the hardness of the end face and referring to the relationship of material hardness Hv-equivalent plastic strain ε _eq -equivalent stress σ _eq . first. The end face of the punched end face was cut out and the Vickers hardness Hv of the cross section was measured. FIG. 6 shows the hardness measurement positions. Here, the indentation load was set to 100 gf, and the measurement was performed at intervals of 0.1 mm at a position 0.08 mm from the punched portion. Next, in order to estimate the plastic strain from the hardness of the punched end surface, the relationship between the plastic strain ε _eq and the Vickers hardness Hv was determined by a tensile test (Fig. 6). Here, the relationship between hardness and plastic strain is Hv = 310 (0.078 + ε _eq ) ^0.122
was approximated by

Furthermore, a tensile test revealed that the material equivalent stress σ _eq -equivalent plastic strain ε _eq relational expression σ _eq = 985 (0.015 + ε _eq ) ^0.122
asked for From this relational expression and the cross-sectional hardness Hv of the sheared end surface, the equivalent plastic strain ε _eq and the equivalent stress σ _eq introduced during shearing were estimated (Fig. 6). Since the stress and strain at the hole edge are uniaxial,
ε _eq = ε _θ , σ _eq = σ _θ
is. A sheared edge consists of shears, a sheared surface, a fractured surface, and burrs. Here, the equivalent plastic strain of the fractured surface to which greater work hardening is introduced is defined as the plastic strain _εbl of the sheared edge.

Furthermore, using a method of estimating the work hardening state during shearing from this cross-sectional hardness, various steel sheets were subjected to _shearing experiments to determine the ratio _d0 / It is also possible to construct a database that associates material/processing factors such as t, material ductility e _t , and punch-to-die clearance c during shearing with the work hardening state. Here, FIG. 7 shows a summary of the results from the 270 MPa class steel plate to the 1470 MPa class steel plate.

On the other hand, in addition to determination by experiment, the equivalent plastic strain ε _eq and the equivalent stress σ _eq can also be determined by, for example, a shear simulation using the finite element method. In this example, the equivalent plastic strain distribution of the sheared edge was analyzed by the ductile fracture theory that can consider the damage and the shearing simulation. Here, Abaqus Explicit, an elasto-plastic finite element method solver, was used for the shear processing simulation, the tool was modeled as a rigid body, and the analysis was performed assuming axisymmetric conditions. The following modified Cockroft equation was adopted as the ductile fracture condition equation.

In the formula, D is the damage value, σ ₁ is the maximum principal stress, σ _eq is the equivalent stress, and ε _eq is the equivalent plastic strain. Elements whose D reached material-specific criteria were judged to be ductile fractures, and crack propagation was expressed by reducing the stiffness of the element. In addition, remeshing was employed to deal with local deformation concentration occurring during shearing. Fig. 8 shows the distribution of equivalent plastic strain obtained by shearing simulation.

In this example, the effect of work hardening during shearing was considered by inputting the material parameters obtained by offsetting the equivalent plastic strain amount estimated based on the work hardening curve of the material into the hole edge element group.

In order to obtain the distribution of circumferential strain ε _θ and radial strain ε _r from the hole edge during the hole expansion deformation process, numerical simulations were performed using finite element FEM. FIG. 9 shows the circumferential strain distribution in the radial direction from the hole edge at punch strokes of 9 mm, 12 mm, 14.2 mm and 15.6 mm.

High approximation accuracy can be obtained by calculating the strain distribution by numerical simulation, but the steps required for constructing a finite element model, etc., are complicated. If high approximation accuracy is not required, the strain distribution may be determined by series expansion, linear approximation, or the like. The series expansion of the strain distribution assumes axially symmetrical deformation, and can be theoretically solved from the balance equations of minute elements as shown in the following equations (6) and (7).

where ξ is the dimensionless radial coordinate, (ε _θ ) _ξ=0 and (ε _r ) _ξ=0 are the circumferential strain and radial strain of the hole edge, b ₁ to c ₂ are constants, and the following equation is given by

Here, n is a material parameter when the work hardening law of the material is approximated to the nth power. In the case of linear approximation, the strain in the circumferential direction and the strain in the radial direction of the hole edge can be obtained from Equation (9), respectively, and approximated so that they become 0 at the outer peripheral portion of the material.

On the other hand, the circumferential strain and radial strain of the hole edge can also be measured by experiment instead of the numerical analysis method described above. A circle or lattice pattern is drawn in advance on the surface of a metal plate by etching or the like, and after a hole expansion test is performed, the critical strain at break is measured from the amount of deformation of the circle.

Next, the circumferential stress distribution σ _θ in the radial direction from the hole edge is calculated. First, from the radial strain ε _r and the circumferential strain ε _θ in the plate surface, the plate thickness direction strain ε _t is obtained from the following volume constant law.
ε _t =−(ε _θ +ε _r )

Further, assuming that the work hardening property of the material follows the n-th power hardening law, the relationship between the equivalent stress σ _eq and the equivalent plastic strain ε _eq is as follows, where c is a constant.
σ _eq =cε _eq ⁿ

Furthermore, the equivalent plastic strain ε _eq is obtained by integrating the equivalent plastic strain increment dε _eq over the strain path. For example, using the von Mises yield function, it can be expressed as follows.

If necessary, a highly anisotropic yield function may be used, but there are many parameters, and it is necessary to consider the direction within the plate surface during processing. is not sufficient, and the yield function assuming in-plane isotropy is sufficient for practical purposes. Furthermore, the stress component in the circumferential direction is expressed by the following equation, assuming isotropic hardening of the yield surface, normality, and plane stress.

Equation (5) is then calculated by piecewise quadrature integrating from the hole edge to the perimeter of the material. For more accurate calculation, since the vertical wall portion is plane strain deformation and the circumferential strain is 0, it is sufficient to integrate up to the connection portion between the punch shoulder and the vertical wall portion. It is assumed that the circumferential stress distribution σ _θ is continuous in the section [d ₀ /2, D ₀ /2] from the hole edge to the outside, and this section is divided into n equal parts. Then, the formula (5) becomes the following formula.

Here, the plate thickness t after deformation can be calculated from the raw plate thickness t ₀ and the plate thickness direction strain ε _t by the following equation.

Circumferential stress σ _θ of the part and the value of the work hardening rate dσ _θ /dε _θ of the material at that time are required to calculate the values in the parentheses in Equation (16). The work hardening rate under uniaxial stress can be obtained from a tensile test, but it is not easy to obtain the work hardening rate under multiaxial stress during deformation experimentally. Therefore, assuming a rigid plastic body, constant volume (incompressible), plane stress, von Mises yielding phase, isotropic hardening by the n-th power hardening law, normal law of strain rate spatial plastic potential and stress, obtained from the tensile test The stress-strain relationship of multiaxial tensile deformation is calculated from the stress-strain curve relationship.

_The circumferential direction and the radial direction in the plate surface _are defined as x1 and x2 _, and the plate surface normal direction is defined as x3. Furthermore, the strain ratio β between the radial direction and the circumferential direction is set as follows and calculated by the following procedure.

The above operation is repeated to calculate the stress-strain relationship under multiaxial tensile deformation up to the large deformation region and the work hardening rate at that time. Then, the plastic instability index I of the hole expansion deformation process can be calculated from these and the equation (16). Here, the material was divided into 21 sections from the hole edge to the outermost periphery, and the plastic instability index was calculated for each section. As an example of the results, FIG. 10 shows the radial distribution of the crack plastic instability index determined by the piecewise quadrature method at punch strokes of 9 mm and 14.2 mm. Furthermore, FIG. 11 shows the relationship between the plastic instability index and the stroke. From FIG. 11, it can be seen that the plastic instability index decreases as the stroke increases. Then, when the value of d (the diameter of the hole after deformation) is such that this value is 0, cracks occur at the edge of the hole. From this it can be calculated that the limiting hole expansion ratio is about 72%.

According to this embodiment, by calculating the damage to the punched portion due to the shearing process, it is possible to predict the forming limit of the hole expansion with high accuracy. Then, it is possible to theoretically calculate the fracture limit hole expansion ratio obtained in the cylindrical hole expansion test from the stress-strain relationship obtained from the tensile test, and by applying this to the forming simulation, the risk of stretch flange fracture can be quantitatively evaluated. As a result, it is possible to avoid stretch flange fracture, which is a forming problem in high-strength steel sheets, and to realize press forming of high-strength and lightweight parts.

(Example 2)
A second embodiment will be described below.
A specific configuration of the present invention will be described as an example of evaluating the moldability of automobile parts with reference to FIG. 12 . Each of the following steps, particularly the first to fifth calculation means in steps S6 to S11, is realized as each function of a central processing unit (CPU) of a computer, for example.

In evaluating the formability of a steel plate that is an automobile part, first, after setting the structure of the automobile (step S1), the shape of the automobile part is set using CAD (step S2), and the three-dimensional part shape is computer-generated. record above (step S3). Here, in order to evaluate whether or not press working can be performed using the mold, the mold is designed using mold CAD (step S4), and software is selected according to the purpose. Record on computer.

Subsequently, the input data for press forming analysis, specifically, the material parameters, plate thickness, forming conditions, and analysis model (finite element model of the tool and raw plate) of the part to be subjected to formability evaluation are set (step S5 ).

Subsequently, the first calculation means theoretically calculates the breaking limit hole expansion ratio obtained by the hole expansion test using the relationship between stress and strain obtained by the tensile test. Specifically, the rupture limit hole expansion ratio is theoretically calculated from the input data for press forming analysis (step S6).

Subsequently, the second calculating means calculates the breaking limit strain of the plate edge, that is, the following breaking criteria ε ^cr =ln(1+λ/100) based on the calculated breaking limit hole expansion rate λ (step S7). . Then, the third calculation means performs molding analysis (step S8) and outputs analysis results (step S9).

The fracture risk ratio is obtained by calculating the ratio ε ₁₁ /ε ^cr of the maximum principal strain ε ₁₁ of each element obtained from the fracture criteria obtained as described above and the results of the simulation of the deformation process by the finite element method. be done. The fourth calculation means calculates the above ratio and determines that the fracture will occur when the maximum principal strain ε ₁₁ reaches the fracture criterion, or that the risk of such fracture is high (step S10).
Thereafter, the fifth calculation means contour-displays the risk of breakage (step S11), and judges the moldability (whether molding is possible). Thus, by continuously executing a series of steps including steps S6 to S11, the formability of the steel sheet is evaluated based on the obtained analysis results.

As a specific example, a saddle-shaped part with a flange height H = 30 mm, a corner R = 30 mm, and an opening angle θ = 120° is molded from a 980 MPa class high-strength steel plate with a thickness of 1.4 mm. FIG. 13 shows the evaluation results.

According to this example, the stress-strain relationship obtained from the tensile test can be theoretically calculated from the rupture limit hole expansion ratio obtained in the cylindrical hole expansion test. The risk of flange breakage can be quantitatively evaluated. As a result, it is possible to avoid stretch flange fracture, which is a forming problem in high-strength steel sheets, and to realize press forming of high-strength and lightweight parts.

(Example 3)
Example 3 will be described below.
A specific configuration of the present invention will be described as an example of evaluating the moldability of automobile parts with reference to FIG. 14 . Each of the following steps, particularly the first to fifth calculation means in steps S6 to S11 and the sixth calculation means in step S16 are implemented as respective functions of a central processing unit (CPU) of a computer, for example.

In this embodiment, as in the second embodiment, steps S1 to S5 are first executed.
Subsequently, damage to the punched portion due to shearing is calculated by the sixth calculation means, and this state quantity is input to the forming analysis (step S16). The sixth calculation means calculates the plastic strain ε _bl and the equivalent stress σ _eq to be introduced to the punched end face by shear simulation, for example.

Thereafter, steps S6 to S11 are executed in the same manner as in the second embodiment. Thus, by continuously executing a series of steps including step S16 and steps S6 to S11, the formability of the steel sheet is evaluated based on the obtained analysis results.

According to this embodiment, by calculating the damage to the punched portion due to the shearing process, it is possible to predict the forming limit of the hole expansion with high accuracy. Then, it is possible to theoretically calculate the fracture limit hole expansion ratio obtained in the cylindrical hole expansion test from the stress-strain relationship obtained from the tensile test, and by applying this to the forming simulation, the risk of stretch flange fracture can be quantitatively evaluated. As a result, it is possible to avoid stretch flange fracture, which is a forming problem in high-strength steel sheets, and to realize press forming of high-strength and lightweight parts.

(Example 4)
Each step (steps S5 to S11 in FIG. 12, steps S16 and steps S5 to S11 in FIG. 14, etc.) of the formability prediction evaluation method according to the present embodiment described above is executed by a program recorded in a computer RAM, ROM, or the like. It can be realized by This program and a computer-readable recording medium recording the program are included in this embodiment.

Specifically, the above program is recorded on a recording medium such as a CD-ROM, or provided to the computer via various transmission media. As a recording medium for recording the above program, a flexible disk, a hard disk, a magnetic tape, a magneto-optical disk, a non-volatile memory card, etc. can be used in addition to the CD-ROM. On the other hand, as the transmission medium for the program, 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 LAN, a WAN such as the Internet, a wireless communication network, or the like, and the communication medium is a wired line such as an optical fiber, a wireless line, or the like.

In addition, the programs included in the present embodiment are not limited to those that realize the functions of the present embodiment by executing the supplied program by the computer. For example, even if the program realizes the functions of the present embodiment in cooperation with an OS (operating system) running on a computer or other application software, such program is included in the present embodiment. In addition, even if all or part of the processing of the supplied program is performed by a function expansion board or function expansion unit of a computer to realize the functions of this embodiment, such program is included in this embodiment.

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

Programs stored in the CPU 1201, ROM 1202, or hard disk (HD) 1211 of the PC 1200 implement steps S5 to S11 in FIG. 12 and steps S16 and S5 to S11 in FIG.

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

A CRT controller (CRTC) 1206 controls display on a CRT display (CRT) 1210 . 1207 is a disk controller (DKC). The DKC 1207 controls access to a hard disk (HD) 1211 and a flexible disk (FD) 1212 that store boot programs, multiple applications, edit files, user files, network management programs, and the like. Here, the boot program is a boot program that starts the execution (operation) of the hardware and software of the personal computer.

A network interface card (NIC) 1208 exchanges data bidirectionally with a network printer, other network equipment, or another PC via a LAN 1220 .
It should be noted that, instead of using the personal user terminal device, a predetermined computer or the like specialized for the formability prediction evaluation method may be used.

Claims (19)

For the thin plate to be tested, from the relationship between the stress and strain obtained by the tensile test ,
In the hole expansion test , D0 is the diameter of the cylindrical punch, _d0 is the initial diameter of the hole in the thin plate, _d is the diameter of the hole in the deformation process of the thin plate, t is the thickness of the thin plate, and t is the thickness of the thin plate. When the circumferential stress in the radial direction from the edge is σ _θ , the work hardening rate is dσ _θ /dε _θ , and the radial coordinate is r,

Calculate the value of d that satisfies the rupture limit hole expansion rate

a first step of theoretically calculating
A second step of calculating the fracture limit strain of the plate end based on the fracture limit hole expansion ratio calculated in the first step;
A third step of evaluating that the risk of fracture is high when the maximum principal strain obtained from numerical analysis by the finite element method reaches the fracture limit strain calculated in the second step,
A formability evaluation characterized in that the first step, the second step, and the third step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. Method. 2. The formability evaluation method according to claim 1 , wherein the circumferential stress in the radial direction from the hole edge of the thin plate is obtained by numerical analysis using a finite element method. 2. A strain distribution in the radial direction and the circumferential direction of the thin plate is obtained by numerical analysis using the finite element method, and the stress in the radial direction from the hole edge of the thin plate is obtained using the strain distribution. The moldability evaluation method described in . 2. The formability evaluation method according to claim 1 , wherein the circumferential stress in the radial direction from the hole edge of the thin plate is obtained by experimenting to obtain the strain distribution of the thin plate and using the strain distribution. 2. The formability evaluation method according to claim 1 , wherein the circumferential stress in the radial direction from the hole edge of the thin plate is obtained by series expansion or linear approximation to obtain the strain distribution of the thin plate, and the strain distribution is used to obtain the strain distribution. . further comprising, prior to the first step, a fourth step of calculating damage to the punch due to shearing;
The first step, the second step, the third step, and the fourth step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. The moldability evaluation method according to any one of claims 1 to 5 . In the fourth step, the hardness of the sheared edge is used to calculate the plastic strain ε _θ introduced to the sheared edge of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate. The moldability evaluation method according to claim 6 . In the fourth step, the relationship between the ratio _d0 /t of the initial hole diameter _d0 of the thin plate and the thickness _t of the thin plate, the ductility et of the thin plate, and the clearance c between the punch and the die during shearing. The formability evaluation method according to claim 6 , wherein the plastic strain ε _θ introduced into the sheared end face of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated using . In the fourth step, the plastic strain ε _θ introduced to the sheared end surface of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated by shear simulation by the finite element method. The moldability evaluation method according to claim 6 . For the thin plate to be tested, from the relationship between the stress and strain obtained by the tensile test ,
In the hole expansion test , D0 is the diameter of the cylindrical punch, _d0 is the initial diameter of the hole in the thin plate, _d is the diameter of the hole in the deformation process of the thin plate, t is the thickness of the thin plate, and t is the thickness of the thin plate. When the circumferential stress in the radial direction from the edge is σ _θ , the work hardening rate is dσ _θ /dε _θ , and the radial coordinate is r,

Calculate the value of d that satisfies the rupture limit hole expansion rate

a first step of theoretically calculating
A second step of calculating the fracture limit strain of the plate end based on the fracture limit hole expansion ratio calculated in the first step;
a third step of assessing that the risk of fracture is high when the maximum principal strain obtained from numerical analysis by the finite element method reaches the fracture limit strain calculated in the second step;
A formability evaluation characterized in that the first step, the second step, and the third step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. program. 11. The moldability evaluation program according to claim 10, wherein the circumferential stress in the radial direction from the hole edge of the thin plate is obtained using numerical analysis using the finite element method. 2. A strain distribution in the radial direction and the circumferential direction of the thin plate is obtained by numerical analysis using the finite element method, and the stress in the radial direction from the hole edge of the thin plate is obtained using the strain distribution. 0 moldability evaluation program. 11. The moldability evaluation program according to claim 10, wherein the strain distribution of the thin plate is determined by experiments, and the circumferential stress in the radial direction from the hole edge of the thin plate is determined using the strain distribution. The formability evaluation according to claim 10, wherein the strain distribution of the thin plate is obtained by series expansion or linear approximation of the circumferential stress in the radial direction from the hole edge of the thin plate, and the strain distribution is used to obtain the strain distribution. program. further comprising, prior to the first step, a fourth step of calculating damage to the punch due to shearing;
The first step, the second step, the third step, and the fourth step are continuously performed as a series of steps, and the formability of the thin plate is evaluated based on the obtained analysis results. The moldability evaluation program according to any one of claims 10 to 14 . In the fourth step, the hardness of the sheared edge is used to calculate the plastic strain ε _θ introduced to the sheared edge of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate. The moldability evaluation program according to claim 15 . In the fourth step, the relationship between the ratio _d0 /t of the initial hole diameter _d0 of the thin plate and the thickness _t of the thin plate, the ductility et of the thin plate, and the clearance c between the punch and the die during shearing. The formability evaluation according to claim 15 , wherein the plastic strain ε _θ introduced to the sheared end face of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated using program. In the fourth step, the plastic strain ε _θ introduced to the sheared end surface of the hole edge and the circumferential stress σ _θ in the radial direction from the hole edge of the thin plate are calculated by shear simulation by the finite element method. The moldability evaluation program according to claim 15 . A computer-readable recording medium having recorded thereon the moldability evaluation program according to any one of claims 10 to 18 .

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