Methods, programs, and recording media for determining the cracking pattern of thin metal sheets when bent.

Abstract

Updated 5 / 01 / 2016 The limiting force when broken from bending (formula) cr will be calculated to find each value from among them. (bending radius R at the center of the sheet thickness of the thin metal sheet) / (initial sheet thickness of the thin material t0); The fracture limit curve L1 is calculated to determine the state in which the deformation is uniform. In free space, stress is applied under conditions regarding the rate of change of static length and the limiting stress. When cracking occurs, the formula l_pl is calculated under deformation due to the rate of length change in the direction. The plane of the characteristic hardening properties of the workpiece is obtained by uniaxial tensile testing of the supplied material. Thin sheet metal structure; the ratio (formula) is determined between the limiting stress at which cracks occur. The bending (formula) cr corresponding to R / t0 of the component to be judged is determined in a thin metal sheet. The limiting stress at fracture (formula) l_pl under deformation due to the rate of length change in the direction A plane in a uniformly deformed state; and a curve showing the limit at crack L2. The ratio corresponding to R / t0 is calculated by multiplying the stress component of the limit curve when The crack L1 is then calculated using the ratio (formula), and the corresponding principal stress (formula) OBcr is then calculated from the principal stress. The OR formula of the components that must pass the determination and the limit curve showing the fracture limit L2. Consistent with the bending amount R / t0 under stress; the risk rate (formula) OR / (formula) OBcr is calculated, which It is the risk of cracking when stretched or bent from a greater value among the stresses (formula) OR and the stress. The limiting factor for cracking (formula) OBcr and the crack determination judgment are performed for the required elements. The decision is made based on the risk rate (formula) OR / (formula) OBcr. ------------------------------------------------------------------------ The limiting stress at bending to break (formula) is calculated to find each value from among the (radius). The bending section R is at the center of the sheet thickness of the thin metal sheet) / (initial sheet thickness of the thin material t0); line. The tear limit curve L1 is calculated to find the state of uniform deformation in the surface. A space subjected to stress under conditions regarding the static rate of change of length and the limiting stress at tearing. The formula is calculated under deformation due to the rate of change in length along the system from its characteristic. Specifically in the hardening of workpieces obtained by uniaxial tensile testing of sheet metal-structured materials. Certainly, a ratio (formula) is determined between the limiting stress at breakage from bending (formula) and the corresponding tearing stress. With R / t0 of the component that must pass the judgment determined in a thin metal sheet, and the limiting stress at tearing (formula). (Formula) Under deformation due to the rate of change of length in the planar direction in the deformed state. The shape is uniform; and the tear limit curve L2 corresponding to R / t0 is calculated by Multiply the stress component of the tear limit curve L1 by the ratio (formula), then the stress. The corresponding principal stress (formula) will be calculated from the principal stress (formula) of the element to be passed through. The determination and the tear limit curve L2 correspond to the bending amount R / t0 in. Under stress conditions, the risk rate (formula) is calculated, which is the risk rate for tearing when... Stretching from the greater value among the stresses (formula) and the limiting stress at tearing (formula); and judgment. The tear-off size schedule will be implemented for the elements requiring judgment, determined based on the rate. Risk (formula);

Description

The present invention relates to a method, program, and storage medium for predicting bending fracture of metal sheets. More specifically, the present invention relates to a method, program, and storage medium for determining the risk of bending fracture of metal sheets in a forming process for press-forming automobile body parts or in a collision deformation process for automobile body parts. In recent years, the application of high-strength steel sheets to automobile bodies has been rapidly progressing due to the demands for improved collision safety and weight reduction. High-strength steel sheets used in automobile bodies can increase the energy absorbed during collisions and improve buckling strength without increasing the sheet thickness. However, as the strength of the steel sheets increases, the ductility and bendability of the steel sheets decrease, which may cause the steel sheets to fracture during press forming and collision deformation. To determine the state of the steel sheets during press forming and collision deformation, there is a growing need for high-precision fracture detection of steel sheets using the finite element method. It is known that the thickness reduction rate or forming limit diagram (FLD) is used to evaluate the margin of safety against fracture during formability and collision performance evaluation. Figure 1 shows an example of FLD in strain fields from uniaxial deformation to plane strain deformation and from plane strain deformation to equibiaxial deformation. As shown in this figure, FLD is a diagram illustrating the relationship between the maximum principal strain and the minimum principal strain that gives the fracture limit. A brief explanation of the experimental method for measuring FLD is given below. First, a metal plate with a circular or grid pattern drawn on its surface by etching or the like is fractured by hydraulic forming or stretching with a rigid tool. Next, the fracture limit strain is determined from the amount of deformation of the pattern on the surface of the fractured metal plate. A load is applied to the metal plate to change the in-plane strain ratio, and the fracture limit strain at each strain ratio is plotted to obtain the fracture limit line. In addition, as theoretical predictions of the FLD, combined use of Hill's local necking model and Swift's diffuse necking model, the Marciniak-Kuczynski method, the Storen-Rice model, etc. are known. Ductile fracture of a material occurs at a position where deformation is localized due to local necking. Since the material fractures in an extremely short time when local necking occurs, the fracture limit is often considered to be the same as the local necking occurrence limit. For this reason, fracture limit prediction is often treated as a problem of plastic instability phenomenon. In the conventional fracture prediction method described in Japanese Patent Application Laid-Open No. 2012-33039, the risk of fracture is predicted by comparing the position relationship between the fracture limit line and the strain state of each element obtained from the simulation by the finite element method. That is, when the strain in the deformation process obtained from the simulation reaches the limit strain defined by the fracture limit line, it is determined that fracture or the risk of fracture is high. As described above, the FLD obtained from experiments or theoretical predictions targets the phenomenon of material separation or the occurrence of local necking under a uniform stress state. However, in the case of bending, there is a large strain gradient from the outer side to the inner side of the bend. FIG. 2 is a diagram for explaining local necking in a uniform stress state, and FIG. 3 is a diagram for explaining the strain gradient in the plate thickness direction of the bent portion. As shown in FIG. 3, in the bent portion, since there is a large strain gradient from the outer side to the inner side of the bend, when the outer side of the bend reaches the fracture condition in the uniform stress state, the inner side of the bend has not reached the fracture condition. Even when the outer side of the bend has reached the fracture condition, due to the supporting effect of the inner side of the bend, the material as a whole may not reach a plastic instability state and may not fracture. The condition that the outer side of the bend has reached the fracture condition but the inner side of the bend has not reached the fracture condition is specific to the bent portion. The occurrence of local necking in the bent portion is different from the occurrence of local necking in a uniform stress state such as uniaxial tension, bulge, and deep drawing shown in FIG. 2. The occurrence of local necking in the bent portion is different from the occurrence of local necking in a uniform stress state, and a method for determining bend fracture in a forming analysis or a collision analysis based on the fracture of the bent portion is not known. The present invention aims to provide a method for determining bending fracture of a metal sheet, which can quantitatively determine the risk of bending fracture from the results of forming analysis or collision analysis using the finite element method, regardless of the properties of the metal forming the metal sheet and the load conditions when the metal sheet is bent. The present invention also aims to provide a program for determining bending fracture of a metal sheet, which can quantitatively determine the risk of bending fracture, and a recording medium on which the program is stored. One aspect of the present invention calculates the bending fracture limit stress for each (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate), calculates the fracture limit line in a uniformly deformed state and the fracture limit stress under plane strain deformation in a stress space assuming a static strain rate from the work hardening characteristics obtained from a uniaxial tensile test of the material constituting the metal plate, determines the ratio of the bending fracture limit stress corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate) for the element to be judged in the metal plate to the fracture limit stress under plane strain deformation, and calculates the fracture limit line corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate) by multiplying the stress component of the fracture limit line in the uniform deformation state by the ratio of the bending fracture limit stress corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate) for the element to be judged to the fracture limit line corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate). A method for determining bending fracture of a metal plate, comprising: calculating the fracture limit stress from the stress of the element to be judged and the fracture limit line corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate); calculating a risk factor which is the ratio of the stress of the element to be judged and the fracture limit stress calculated from the stress of the element to be judged and the fracture limit line corresponding to (bending radius at the center of the thickness of the metal plate) / (initial thickness of the metal plate); and determining fracture of the element to be judged based on the risk factor. According to the above embodiment, fracture determination of the target element of the metal plate is performed based on the risk factor calculated as described above. That is, it can be determined that the metal plate has fractured when the risk factor reaches 1.0, and the closer the risk factor is to 1.0, the smaller the margin of safety before the metal plate fractures. Furthermore, in the present invention, the fracture limit line obtained from a uniaxial tensile test is corrected by the above ratio to calculate the fracture limit line, and the fracture limit stress of the target element is determined based on this corrected fracture limit line. Therefore, compared to simply determining the fracture limit stress of the target element based on the fracture limit line obtained from a uniaxial tensile test, a more accurate fracture determination of the metal plate can be performed. The present invention has the excellent effect of being able to quantitatively determine the risk of bending fracture from the results of forming analysis or collision analysis using the finite element method. This figure shows an example of a forming limit diagram. This figure illustrates local necking under uniform stress conditions. This figure illustrates the strain gradient in the thickness direction of the bent section. This figure illustrates a V-bending test with an opening of 90°. This figure illustrates a tensile bending test. This figure illustrates the difference in strain conditions between pure bending and tensile bending. This figure shows the relationship between true stress and true strain when R / t0 is 2.0. This figure shows the bending fracture limit stress σcr for each bending amount R / t0. This figure shows the fracture limit line indicated in stress space. This figure illustrates the process of determining the fracture limit line corresponding to the bending amount R / t0 from the fracture limit line under uniform stress conditions indicated in stress space. This figure illustrates the process of determining the second criticality factor F2 = σOR / σOBcr. This figure shows a part of the flowchart of the algorithm executed by the fracture determination device. This figure shows another part of the flowchart of the algorithm executed by the fracture determination device. This is a schematic diagram showing the internal configuration of a personal user terminal device. This figure shows the calculation conditions for the three-point bending collision analysis used in an embodiment of the present invention. This figure shows the fracture risk obtained using the present invention as contour lines for a three-point bending collision analysis used in an embodiment of the present invention. One embodiment of the present invention will be described in detail below with reference to the drawings. (Basic Idea) When bending deformation occurs in a metal sheet made of a metallic material, the circumferential tensile stress decreases from the outside to the inside of the bend, while the radial compressive stress increases. As the bending progresses, the magnitude and stress state of these stresses change. However, since the stress and strain generated by bending are not uniformly distributed in the thickness direction of the sheet, the local necking condition that is applied to uniform distributions cannot be applied. Because the local necking condition for uniform distributions cannot be applied to fracture determination of the bent portion, conventional fracture determination of the bent portion using forming simulations and collision simulations, which have been widely used, cannot be said to have sufficient practical reliability. Therefore, we investigated a bending fracture determination method that can determine the risk of bending fracture from the results of forming analysis and impact analysis using the finite element method in press forming or impact deformation that undergoes bending deformation with a strain gradient in the thickness direction of the plate. The mechanism of bending fracture can be broadly classified into two types based on the fracture mode. The first type of fracture mode is one in which a crack occurs on the outer surface of the bend without the appearance of a clear local necking. The second type of fracture mode is one in which no crack occurs on the outer surface of the bend, but a significant reduction in plate thickness (local necking) is observed at the tip of the bend before fracture occurs. In order to predict bending fractures occurring in these two different types, (1) a first significance level is determined using the bending surface limit stress, which is obtained by converting the bending surface limit strain into stress, as the criterion, and (2) -1: the fracture limit stress for each bending radius is determined from the theoretical solution of the stress-strain relationship in plane strain tensile bending, and the tensile bending fracture limit stress under plane strain deformation is determined for each element (bending radius R at the center of plate thickness) / (initial plate thickness t0) according to the necking occurrence condition (dσ1 / dε1 = σ1), which will be described in detail later, and ( 2)-2: The inventors have developed a metal plate fracture determination method in which the fracture of the metal plate is determined based on the larger of the first and second risk factors. This method involves comparing (2)-3: determining the criteria in stress space by assuming a static strain rate from the work hardening characteristics obtained from a uniaxial tensile test of the material, and using the bending fracture limit line in stress space, which is determined by offsetting the criteria obtained in (2)-2 under plane strain deformation, as the criterion. The first risk factor will be explained first, followed by the second risk factor. In the following, (bending radius R) / (initial plate thickness t0) will simply be referred to as bending amount R / t0. (First Risk Factor) The first risk factor, which uses the bending surface limit stress as its criterion, is a method for evaluating fracture modes commonly seen in V-bending tests with a 90° opening, as shown in Figure 4, and is known as a method for evaluating the bendability of high-strength steel plates. In the bending test to evaluate the first risk factor, a rectangular test piece G cut from the test steel plate is used so that the longitudinal direction is perpendicular to the rolling direction. The longitudinal center of the rectangular test piece G is pressed into a V-shaped die with a 90° opening using multiple punches P with predetermined tip radii (for example, 0.5 mm to 6.0 mm). The minimum bending radius is determined from among the punch tip radii that do not produce any fine cracks that can be visually determined on the surface of the rectangular test piece G pressed into the die. Incidentally, it is known that the bendability of high-strength steel sheets does not correlate with total elongation and n-value, but corresponds well with the microstructure homogeneity index (see "Kazumasa Yamazaki et al.: Plasticity and Processing, 36-416 (1995), 973."). In other words, in composite steel sheets with heterogeneous structures, the hard parts hinder strain propagation, causing strain concentration, and due to the low deformability of the hard parts themselves, the hard parts are thought to be the starting point for cracks. On the other hand, it is known that steel sheets with a homogeneous structure, even those largely composed of a martensite phase with low deformability, exhibit good bendability. In the embodiment of the present invention, in order to evaluate the occurrence of cracks in the surface layer due to microstructure heterogeneity, we focused on the material-specific bending surface limit strain (also called the bending outer limit strain), and adopted the bending surface limit stress, which is this bending surface limit strain converted into stress, as the fracture judgment criterion. The limit stress at the bending surface is obtained for each steel material through bending tests such as the V-bending test described above and simulations based on those tests. Note that the bending test is not limited to a V-bending test with a 90° opening; other test methods may be used, such as a 180° bending test or measuring the minimum bending radius by L-bending, where the steel material is bent into an L-shape using a punch and die. The limiting stress at the bending surface can be determined by simulation using the finite element method, which models a punch with the minimum bending radius obtained from a bending test. It is preferable to use a static implicit method code formulated with plane strain elements and to simulate with small element sizes to represent local strain concentration at the surface. However, the finite element method may also use shell elements formulated in a plane stress state, ensuring at least five numerical integration points in the thickness direction and using elements divided to a size approximately equal to the thickness of the plate. Furthermore, by conducting bending tests using a V-shaped punch, the minimum bending radius at the fracture limit can be determined, and the bending limit surface strain ε0 θ can be calculated from the material's plate thickness t0, inner bending radius ri, outer bending radius r0, and neutral bending radius Rn. In addition to obtaining it through simulations and calculations, the fracture limit surface strain after bending can also be determined from lines on which a grid has been pre-transferred onto the material before deformation. For example, if the grid spacing before deformation is L0 and the spacing after deformation is L, then the bending limit surface strain ε0 θ is Next, assuming a static strain rate, the equivalent stress-equivalent strain relationship obtained from the uniaxial tensile test is used to convert the bending limit surface strain ε0 θ obtained above into the bending limit surface stress σ1 cr. Furthermore, the maximum principal strain ε1 of the surface corresponding to the outer side of the bending is calculated from the surface strain tensor for each finite element described in the local coordinate system, and this maximum principal strain ε1 of the surface is converted into the maximum bending surface principal stress σ1. Then, as shown in the following equation, the ratio of the maximum bending surface principal stress σ1 to the bending limit surface stress σ1 cr is the first critical factor F1. (Second Risk Level) The fracture mechanism in a tensile bending test can be considered as follows. That is, as shown in Figure 6, in the case of pure bending where only a bending moment acts, the circumferential strain decreases from the outside to the inside of the bend, while the radial compressive strain increases. In contrast, as shown in Figures 5 and 6, in the case of tensile bending where tension and bending moment act simultaneously, the tension causes the neutral plane to move inward, reducing the plate thickness and introducing plastic strain in the tensile direction. After the introduction of plastic strain in the tensile direction, if the tension increases further, the work hardening rate of the material decreases due to tensile deformation. When the work hardening rate decreases, hardening commensurate with the reduction in plate thickness cannot be obtained, so the deformation becomes localized, leading to localized necking and then fracture. Also, even when the same tension is applied, the neutral plane moves further inward as the bending radius decreases. As the neutral plane shifts further inward during bending, strain localization becomes more likely, leading to a significant reduction in plate thickness (localized necking) at the bending tip before fracture occurs. To explain the process leading to the fracture described above, we will first describe the bending plastic instability under tension. We consider the plastic instability conditions under plane strain deformation where a tension of Q and a bending moment of M per unit width are acting, causing local necking. Here, (1) the deformation of the bent portion is assumed to be uniform bending and shear deformation is not considered, (2) it is plane strain deformation, (3) it follows the constant volume rule, (4) the yield function of von Mises is used, and (5) the relationship between equivalent stress and equivalent plastic strain is approximated by the n-th power hardening rule, so it can be expressed as σeq = cεn eq. From these conditions, the circumferential stress distribution σθ and the radial stress distribution σr are given by the following equations. Furthermore, for known q, material thickness t0, and inner bending radius ri, equation [3] and the conditional equation for the constant volume rule are given. As mentioned above, the tension qcr and the fracture limit curvature (1 / ρ) can be used as thresholds for fracture determination. However, considering that the threshold for the first criticality, which is the maximum principal stress σ1 cr at the bending surface, is in the dimension of stress, it is possible to perform more accurate fracture determination if the threshold for the second criticality, which is compared to the first criticality, is also in the dimension of stress. Based on the above, we determine the bending fracture limit stress σOB cr, which is the criterion for calculating the second risk factor. (2)-1 First, the fracture limit stress for each bending amount R / t0 is determined from the theoretical solution of the stress-strain relationship in plane strain tensile bending. The true stress σ1 in the plane strain tensile direction of the bending surface is given by the following equation. Note that R represents the bending radius of the plate thickness centerline. Furthermore, the calculation of the work hardening rate and the conditions for neck formation under plane strain tensile stress are given by the following equation Next, we calculate the bending fracture limit stress σcr for each bending amount R / t0. Figure 7 shows the relationship between true stress and true strain when R / t0 is 2.0. As shown in this figure, we calculate σ1, i.e., the bending fracture limit stress σcr, which satisfies the above necking condition (dσ1 / dε1 = σ1). Then, as shown in Figure 8, we calculate the bending fracture limit stress σcr for each bending amount R / t0. (2)-2 Next, we determine the criteria in stress space, assuming a static strain rate, from the work hardening characteristics obtained from the uniaxial tensile test of the material. First, the work hardening characteristics of the uniaxial tensile test are expressed by the following equation, and from this equation we determine the fracture limit stress in stress space. For example, σeq is If so, the fracture limit stress can be obtained using the principal stress ratio (α = σ² / σ¹) and the work hardening coefficient of the material n = n* - ε₀ as follows: Figure 9 shows the FLD obtained from a uniaxial tensile test. As shown in this figure, the fracture limit line L1 can be obtained by changing the constant α in this equation between 0 and 1 (by changing the principal stress ratio). Here, we have described a method for determining the fracture limit line L1 expressed in stress space from the work hardening characteristics obtained from a uniaxial tensile test of the material, but the fracture limit line L1 can also be determined by converting the measured strain space FLD to stress space as follows. The strain space FLD is a figure showing the maximum principal strain ε11 that gives the fracture limit for each minimum principal strain ε22, and the plate thickness strain ε33 can be determined from these and the constant volume rule ε33 = -(ε11 + ε22). Here, if we use the yield function of von Mises on the yield surface, the equivalent plastic strain is, From the above, the fracture limit line L1 expressed in stress space can be calculated. Alternatively, the fracture limit line L1 can also be determined by converting the FLD in strain space, which was theoretically obtained, into stress space. For example, if the work hardening law of the material is approximated by the nth power law, In equations 20 to 22 above, by varying the constant ρ between -0.5 and 1, the FLD in strain space can be obtained, and by converting this to stress space using the method described above, the fracture limit line L1 in a uniform deformation state in stress space can be determined. Note that ρ represents the plastic strain rate ratio. (2)-3 Next, under plane strain deformation, the tensile bending fracture limit line L2 under plane strain deformation is determined by offsetting the criteria (fracture limit line L1) determined in (2)-2 above. Specifically, as shown in Figure 10, the fracture limit line L2 can be obtained by offsetting the fracture limit line L1 (forming limit diagram) obtained in (2)-2 so as to correspond to the fracture limit stress σcr for each bending amount R / t0 determined in (2)-1 above. In summary, the ratio γ between the bending limit stress σcr corresponding to the bending amount R / t0 of the element to be judged in the metal plate and the plane strain limit stress σ1_pl in a uniformly deformed state is determined, and the fracture limit line L2 corresponding to the bending amount R / t0 is calculated by multiplying the stress component of the fracture limit line L1 by this ratio γ. In Figure 11, along the fracture limit line L2 for tensile bending, the points indicated by the symbol R represent the stress states obtained by converting the plastic strain tensor to a stress tensor, assuming a static strain rate, for all elements under evaluation. The intersection points of the line passing through the origin and R with the fracture limit line L2 are indicated by the symbol B, and the points indicated by the symbol B represent the bending fracture limit stress state of the elements under evaluation. The ratio of these stresses σOR to the fracture limit stress σOB cr is the second risk factor F2. (Method and program for determining bending fracture of a metal plate) Next, a method for determining bending fracture of a metal plate according to an embodiment of the present invention will be described. Figures 12A and 12B are flowcharts showing the algorithm executed by a fracture detection device according to an embodiment of the present invention. The fracture detection device uses a computer program having the algorithms shown in Figures 12A and 12B. This program comprises an extraction means 10, a bending radius calculation means 20, a fracture determination criterion calculation means 30, and a determination means 40, and has the function of causing a computer to execute each of these means. The extraction means 10 performs the process of step S10, which obtains the plate thickness and strain tensors on the front and back surfaces of each element during deformation by forming analysis or impact analysis. The bending radius calculation means 20 performs the process of step S20, which calculates the bending radius of each element from the forming analysis or impact analysis. The fracture determination criterion calculation means 30 performs the process of step S30, which calculates the fracture determination criterion based on the input material parameters. The determination means 40 calculates a first risk rate F1, which is the risk rate of bending surface cracking for each element, and a second risk rate F2, which is the risk rate of tensile bending fracture, and performs the process of step S40, which makes a fracture determination for the fracture mechanism with the higher fracture risk rate among the first and second risk rates. First, in step S10, the extraction means 10 calculates the plate thickness t and strain tensors on the front and back surfaces for each element during the deformation process using a numerical analysis program such as the finite element method, and inputs the calculation results into a user subroutine or external program that determines bending fracture. Next, in step S21, the bending radius calculation means 20 calculates the curvature of each component, as well as the maximum and minimum curvature in the plane, for the element to be determined from the element-specific strain tensor described in the local coordinate system and the plate thickness of the element under deformation. Then, in step S22, the bending radius calculation means 20 calculates the minimum bending radius R of the three-dimensional curved surface. Next, in step S31, the fracture criterion calculation means 30 obtains the material-specific bending limit surface strain ε0 θ obtained from the minimum bending radius for each steel material obtained from experiments such as V bending or L bending at an opening of 90°. Then, assuming a static strain rate, the bending limit surface strain ε0 θ is converted to the bending limit surface stress σ1 cr. Also in step S31, the fracture criterion calculation means 30 obtains the relationship between the equivalent stress σeq and the equivalent plastic strain εeq, σeq = f(εeq), and rm, which is an index of plastic anisotropy. A higher-order polynomial of εeq or other forms may be used as the work hardening function f(εeq), but it is preferable to use the n-th power hardening rule or Swift's formula, which have high approximation accuracy and are often used in forming simulations and collision simulations. Next, in step S32, the fracture criterion calculation means 30 calculates the bending fracture limit stress σcr for each bending amount R / t0 from equations

[12] and

[13] . Next, in step S33, the criteria in the stress space assuming a static strain rate are determined from the work hardening characteristics obtained from the uniaxial tensile test of the material. That is, the fracture limit stress σ1_pl and the fracture limit line L1 shown in Figure 9 are determined from equations

[14] to

[17] . Then, in step S34, the ratio γ (see equation

[23] ) corresponding to the bending amount R / t0 of the element to be judged is determined, and the fracture limit stress σ1_b under plane strain stress is determined. Furthermore, the ratio γ of the bending fracture limit stress σcr corresponding to the bending amount R / t0 of the element to be judged in the metal plate and the plane strain fracture limit stress σ1_pl in a uniformly deformed state is determined, and the fracture limit line L2 corresponding to the bending amount R / t0 is calculated by multiplying the stress component of the fracture limit line L1 by this ratio γ. Next, in steps S41 to S46, the determination means 40 calculates the fracture risk rate for all elements to be determined, and displays the value of the fracture risk rate F as a contour in post-processing. First, in step S41, the determination means 40 calculates the maximum principal strain ε1 of the surface corresponding to the outside of the bending from the surface strain tensor of each finite element described in the local coordinate system, and converts this maximum principal strain ε1 of the surface into the maximum principal stress σ1 of the bending surface. Next, in step S42, the determination means 40 calculates the first risk factor F1 = σ1 / σ1 cr, which is the risk factor for bending surface cracks, from the bending limit surface stress σ1 cr for each steel material and the magnitude of the maximum principal stress σ1 of the bending surface for each element obtained in step S31. Next, in step S43, the determination means 40 calculates the stress σOR under plane strain stress of the finite element and calculates the fracture limit stress σOB cr corresponding to the stress ratio of the finite element from the fracture limit stress σ1_b calculated in step S34. Next, in step S44, the determination means 40 calculates the second risk factor F2 = σOR / σOB cr, which is the risk factor for tensile bending fracture, from the magnitudes of the stress σOR and fracture limit stress σOB cr calculated in step S34. Next, in step S45, the determination means 40 determines that the larger of the first risk factor F1 calculated in step S42 and the second risk factor F2 calculated in step S44 is the risk factor for bending fracture. Then, in step S46, the determination means 40 displays the value of the fracture risk factor index F as a contour by post-processing. Thus, the bending fracture determination method of this embodiment makes it possible to determine the fracture risk for two different types of bending fractures: one in which a crack occurs on the outer surface of the bend without a clear localized constriction, and another in which no crack occurs on the outer surface of the bend, but a significant reduction in plate thickness (localized constriction) is observed at the tip of the bend before fracture occurs. This makes it possible to quantitatively determine which fracture mechanism is more likely to occur and the danger when fracture occurs, for complex phenomena such as press forming and deformation during collision. As a result, it becomes possible to select structures and materials, etc., at the design stage to prevent steel plate fracture, enabling the digital development of lightweight and collision-safe vehicle bodies. Each mechanism constituting the determination device according to this embodiment and each step constituting the determination method according to this embodiment, as described with reference to Figures 12A and 12B, can be realized by operating based on a program stored in the RAM and ROM of a computer. A program for executing each step constituting the determination method according to this embodiment and a computer-readable recording medium on which the program is recorded are included in the embodiments of the present invention. Specifically, the program for executing each step of the determination method according to this embodiment is recorded on a recording medium such as a CD-ROM or provided to a computer via various transmission media. The recording medium on which the program for executing each step of the determination method according to this embodiment is recorded may be a flexible disk, hard disk, magnetic tape, magneto-optical tape, non-volatile memory card, etc. Furthermore, the transmission medium for the program for executing each step of the determination method according to this embodiment can be a communication medium in a computer network system that propagates and supplies program information as a carrier wave. The computer network may be a LAN, a WAN such as the Internet, a wireless communication network, etc., and the communication medium may be a wired line such as an optical fiber and a wireless line, etc. Furthermore, the programs included in this embodiment are not limited to those in which the above-mentioned functions are realized by a computer executing the supplied program. For example, a program used in cases where each step constituting the determination method according to this embodiment cooperates with an OS (operating system) or other application software running on a computer to realize the above-mentioned functions is included in this embodiment. Also, a program used in cases where all or part of the processing of the supplied program is executed on a computer's function expansion board or function expansion unit to realize the above-mentioned functions is included in this embodiment. Figure 13 is a schematic diagram showing the internal configuration of a personal user terminal device. The personal computer (PC) 1200 is equipped with a CPU 1201. The PC 1200 executes device control software stored in ROM 1202 or hard disk (HD) 1211 or supplied by a flexible disk drive (FD) 1212. The PC 1200 comprehensively controls each device connected to the system bus 1204. The strength determination system is realized by the CPU 1201 and the programs stored in ROM 1202 or hard disk (HD) 1211 of the PC 1200. The RAM 1203 functions as the main memory and work area of ​​the CPU 1201. The keyboard controller (KBC) 1205 controls instruction input from the keyboard (KB) 1209 and other devices not shown. The CRT controller (CRTC) 1206 controls the display of the CRT display (CRT) 1210. The disk controller (DKC) 1207 controls access to the hard disk (HD) 1211 and flexible disk drive (FD) 1212, which store the boot program, multiple applications, editing files, user files, and network management programs. Here, the boot program is the startup program that starts the execution of the PC's hardware and software. The NIC 1208 performs bidirectional data communication with network printers, other network devices, and other PCs. In the above-described method for determining bending fracture of a metal plate, an example has been explained in which the larger of the first risk factor F1 and the second risk factor F2 is determined as the risk factor for bending fracture. However, the present invention is not limited to this. For example, in cases where it is not necessary to consider a fracture mode in which a crack occurs on the outer surface of the bend without the appearance of a clear local constriction (for example, in the case of a steel plate with sufficient ductility), only the risk factor corresponding to the second risk factor F2 can be used as the risk factor for bending fracture. (Examples) Examples of the present invention are described below. The fracture determination method according to this embodiment was applied to a three-point bending collision analysis of a frame having a hat cross-section shape, and the effectiveness of the bending fracture determination method for the metal plate was investigated. Figure 14 shows the three-point bending drop load test conditions and the collision analysis calculation conditions used in the embodiment of the present invention. The frame studied was a 900 mm long component with a closed section formed by a hat component and a closing plate. The test material was a 1.8 mm thick high-strength steel plate, and the hat component and closing plate were fastened together at the flange portion by spot welding at a 30 mm pitch. A 500 kg weight was dropped from a height of 3 m onto this specimen, impacting it at an initial velocity of 7.7 m / s. As a result, (1) from the start of the impact until the maximum reaction force was observed, the member deformed along the load, (2) thereafter the wall surface deformed outward and the reaction force began to decrease as it transitioned to a longitudinal bending mode, and (3) the reaction force decreased monotonically as the deformation progressed. Upon observation of the specimen after the test, cracks were observed in the locally deformed area that bent into a V shape. Figure 15 is a contour map showing the fracture risk, determined using the bending fracture determination method for the metal plate, for a three-point bending impact analysis used in an embodiment of the present invention. Figure 15 shows the fracture risk (the larger of the first risk factor F1 and the second risk factor F2) displayed as contour lines. As shown in Figure 15, the higher the risk of fracture, the greater the risk of fracture. When the larger of the first risk factor F1 and the second risk factor F2 reaches 1.0, it can be determined that the material has fractured. The analysis shows that the risk of fracture is high at the bent section where cracks occurred in the drop-load test, and that the analysis reproduces the experiment well. This method for determining the bending fracture of metal plates allows for the quantitative determination of the risk of fracture during deformation in a collision. This enables the consideration of structures and material selections that prevent steel plate fracture during the design phase, thus facilitating the digital development of lightweight vehicle bodies with superior collision safety. Preferred embodiments of the present invention are described below. The method for determining bending fracture of a metal plate according to the first aspect calculates the bending fracture limit stress σcr for each bending amount R / t0 of the metal plate, calculates the fracture limit line L1 in the stress space of the uniform deformation state assuming a static strain rate from the work hardening characteristics obtained from the uniaxial tensile test of the material constituting the metal plate, and calculates the fracture limit stress σ1_pl under plane strain deformation, determines the ratio γ between the bending fracture limit stress σcr corresponding to the bending amount R / t0 of the determination target element in the metal plate and the plane strain fracture limit stress σ1_pl of the uniform deformation state, calculates the fracture limit line L2 corresponding to the bending amount R / t0 by multiplying the ratio γ by the stress component of the fracture limit line L1, calculates the maximum principal stress σOB cr from the maximum principal stress σOR of the determination target element and the fracture limit line L2 corresponding to the bending amount R / t0 in the stress mode, calculates the risk rate σOR / σOB cr, which is the risk rate of tensile bending fracture, from the magnitudes of the stress σOR and the fracture limit stress σOB cr, and performs fracture determination of the determination target element based on the risk rate σOR / σOB cr. According to the above aspect, fracture determination of the determination target element of the metal plate is performed based on the risk rate σOR / σOB cr calculated as described above. That is, it can be determined that the metal plate breaks when the risk rate σOR / σOB cr reaches 1.0, and it can be determined that the margin until the metal plate breaks is smaller as the risk rate σOR / σOB cr approaches 1.0. Further, in this aspect, the fracture limit line L2 is calculated by correcting the fracture limit line L1 obtained from the uniaxial tensile test with the above ratio γ, and the fracture limit stress σOB cr of the determination target element is determined based on this fracture limit line L2. Therefore, compared with the case where the fracture limit stress of the determination target element is determined simply based on the fracture limit line L1 obtained from the uniaxial tensile test, fracture determination of the metal plate with high accuracy can be performed. The method for determining bending fracture of a metal plate according to the second aspect is, in the first aspect, to obtain the bending limit surface strain ε0θ specific to the material constituting the metal plate, convert the bending limit surface strain ε0θ into the bending limit surface stress σ1cr, calculate the maximum principal strain ε1 of the surface layer corresponding to the outer side of the bending of the determination target element, and assume a static strain rate from the maximum principal strain ε1 of the surface layer to convert it into the bending surface maximum principal stress σ1 from the relational expression of the equivalent stress and equivalent strain obtained from a uniaxial tensile test. Calculate the first risk rate F1 = σ1 / σ1cr, which is the risk rate of the bending surface crack, calculate the second risk rate σOR / σOBcr, which is the risk rate σOR / σOBcr, compare the first risk rate F1 = σ1 / σ1cr with the second risk rate σOR / σOBcr, and determine which of the first risk rate F1 = σ1 / σ1cr and the second risk rate σOR / σOBcr is larger. When it is determined that the first risk rate F1 = σ1 / σ1cr is large, perform the fracture determination of the determination target element based on the first risk rate F1 = σ1 / σ1cr. When it is determined that the second risk rate σOR / σOBcr is large, perform the fracture determination of the determination target element based on the second risk rate σOR / σOBcr. According to the above aspect, it is possible to determine the respective fracture risk rates for bending fractures that occur due to two different mechanisms: a fracture mode in which a crack occurs on the outer surface of the bend without the appearance of a distinct local constriction, and a fracture mode in which no crack occurs on the outer side of the bend but fracture occurs after a significant reduction in plate thickness (local constriction) is observed at the tip of the bend. The method for determining bending fracture of a metal plate according to the third aspect is, in the second aspect, the bending fracture limit stress σcr is According to the above aspect, by performing calculations based on the above calculation formula, the bending fracture limit stress σcr and the fracture limit line L1 can be obtained. The fourth embodiment of the method for determining bending fracture of a metal plate is as follows: In the first and second embodiments, the fracture limit line L1 is calculated by converting a fracture limit line expressed in strain space measured from an experiment into a fracture limit line expressed in stress space assuming a static strain rate, or by converting a fracture limit line in strain space theoretically estimated from a stress-strain curve obtained from uniaxial tension into stress space assuming a static strain rate. In the above embodiment, the fracture limit line L1 can be obtained in the same way as in the third embodiment. Furthermore, bending fracture determination of a metal plate can also be performed by having a computer execute a computer program that performs the bending fracture determination method of the metal plate according to the first to fourth embodiments described above. Furthermore, it is possible to create a recording medium on which the above-mentioned computer program is recorded and which is also computer-readable. Although one embodiment of the present invention has been described above, the present invention is not limited to the above and should be judged based on the description of the claims. Furthermore, the disclosure of Japanese Patent Application No. 2013-134199, filed on June 26, 2013, is incorporated herein by reference in its entirety.