Molding limit decision method for metal plate, molding limit decision system for metal plate and molding limit decision program for metal plate

Abstract

To provide a molding limit decision method for metal plate, a molding limit decision system for metal plate and a molding limit decision program for metal plate that can conduct a molding test on a test piece of a metal plate to precisely decide the molding limit of the metal plate.SOLUTION: A molding limit decision method for metal plate includes: constructing a database by molding a metal plate while consecutively photographing a surface of a test piece 101 and measuring strains generated on the surface of the test piece 101 from the start of the molding until fracture and three-dimensional coordinates on the surface of the test piece 101 (S10); setting an evaluation point array along a fracture orthogonal direction orthogonal to a fracture part 103 generated in the test piece 101 and extracting strains or three-dimensional coordinates of the evaluation point array from the database (S20); and calculating a fracture orthogonal-directional gradient of the strains or three-dimensional coordinates of the evaluation point array to decide a molding limit (S30).SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for determining a forming limit of a metal sheet, a system for determining a forming limit of a metal sheet, and a program for determining a forming limit of a metal sheet. [Background technology]

[0002] Metal sheets (e.g., thin steel sheets) used as materials for automobile bodies are mostly processed into body parts by press forming. The press formability of body parts varies depending on the shape of the body part and is also greatly affected by the material properties, such as the ductility of the metal sheet used as the material. In recent years, in response to demands for lighter car bodies, efforts have been made to increase the strength of metal sheets used in body parts. However, as the strength of metal sheets increases, their ductility decreases, making them more susceptible to cracking during press forming and reducing their press formability.

[0003] To avoid problems such as cracks during the manufacture of auto body parts by press forming, it is becoming increasingly important to design dies based on advance predictions of press formability using CAE (Computer Aided Engineering).As a result, technology that can accurately determine the forming limits of metal sheets is becoming increasingly important.

[0004] Forming limit diagrams (FLDs) are usually used to determine the forming limits of metal sheets. Forming limit diagrams are created by measuring the forming limits of various deformation modes of metal sheets in press forming, such as equibiaxial deformation, non-uniform biaxial deformation, plane strain deformation, and uniaxial deformation, through laboratory-scale forming tests. To create a forming limit diagram, the width of the test specimen is varied at several levels, and the strain ratio in the major and minor axes of the test specimen is changed, thereby measuring the strain in both the major and minor axes at the time of fracture.

[0005] Generally, in metal sheet forming tests, the metal sheet specimen undergoes uniform deformation, followed by a process in which strain is concentrated at specific locations on the specimen. During this process, a reduction in thickness, called necking, occurs at the location where strain is concentrated. After this reduction in thickness has progressed, the metal sheet fractures. In press forming, the occurrence of necking can result in a defective product even if it does not lead to fracture. Therefore, the forming limit of metal sheets must be defined using the strain just before necking occurs. In particular, in press forming of high-strength steel sheets with tensile strengths exceeding 980 MPa, necking occurs at a low strain of about 10%, and fracture occurs immediately thereafter. Therefore, the forming limit of high-strength steel sheets must be determined accurately, and several techniques for this purpose have been proposed.

[0006] Non-Patent Document 1 standardizes a method for identifying forming limit curves. In this method, first, the strain distribution around the fracture of a test piece formed until fracture is measured. Next, the measured strain distribution is approximated to the curve of the following equation (1). Then, the maximum value of strain is calculated from equation (1), and this maximum value is taken as the forming limit strain.

number

[0007] However, the method of Non-Patent Document 1 does not directly measure the forming limit strain, and therefore it is sometimes impossible to adequately approximate the strain at the fracture occurrence point and determine the forming limit strain. Therefore, the method of Non-Patent Document 2 has been proposed as an improvement over the method of Non-Patent Document 1. The method of Non-Patent Document 2 involves continuously measuring the strain generated in a test piece during forming, and determining the forming limit strain from the change over time in the strain at the fracture occurrence point. [Prior art documents] [Non-patent literature]

[0008] [Non-Patent Document 1] ISO 12004-2:2008, Metallic materials - Sheet and strip - Determination of forming-limit curves, 2008. [Non-patent document 2] W Hotz, M Merklein et al., “Time Dependent FLC Determination Comparison of Different Algorithms to Detect the Onset of Unstable Necking before Fracture”, Key Engineering Materials, Vol 549, pp.397-404(2013). Summary of the Invention [Problem to be solved by the invention]

[0009] Non-Patent Document 1 describes the Nakajima method and the Marciniak method as methods for determining the forming limit by an extension test of a test piece 101, as shown in FIG. As shown in Figure 11(a), the Nakajima method involves bulging a test piece 101 using a molding die 201 equipped with a spherical punch 203 having a spherical tip 203a, an upper die 205, and a blank holder 207. On the other hand, the Marciniak method, as shown in Figure 11(b), uses a forming mold 211 equipped with a flat-head punch 213 with a flat tip 213a, an upper die 205, and a blank holder 207, and sandwiches a driving sheet 215 between the flat-head punch 213 and the test piece 101 to bulge-form the test piece 101.

[0010] In the Nakajima method, the test piece 101 is stretch-formed in a state where it conforms to the shape of the tip 203a of the ball-head punch 203. Therefore, the obtained forming limit (maximum principal strain and minimum principal strain at fracture) is affected by the bending deformation of the test piece 101. In contrast, in the Marciniak method, the test piece 101 is stretch-formed using a flat-head punch 213. Therefore, the test piece 101 is not bent, and the resulting forming limit is not affected by the bending deformation of the test piece 101.

[0011] Therefore, when comparing the Nakajima method and the Marciniak method, the forming limit line obtained by the Nakajima method generally has a strain just before necking occurs that is approximately 1 to 2% larger, as shown in Figure 11(c).

[0012] In press forming of high-strength steel sheets with low ductility, slight differences in strain can lead to differences in the occurrence of necking. Therefore, until now, the forming limit of metal sheets has been evaluated by comparing the forming limit diagrams of the Nakajima method and the Marciniak method based on the strain measured in actual press-formed products and the strain obtained from press forming analysis using CAE.

[0013] However, even under press forming conditions where the Nakajima method predicted no cracking based on the strain amount obtained from press forming analysis, cracks sometimes occurred in actual press formed metal sheet products, especially in actual press formed products of high strength steel sheets of 980 MPa class or higher.Furthermore, even under press forming conditions where the Marciniak method predicted cracking, cracks sometimes did not occur in the actual press formed products.

[0014] As described above, there have been many cases where the predicted results of cracking based on press forming analysis using forming limit diagrams differed greatly from the actual occurrence of cracking in press-formed products, which has been problematic.

[0015] It is also known that the strain distribution of a test piece in a stretch test changes depending on the work hardening rate (n value) of the material. Therefore, in order to determine the forming limit using the method in Non-Patent Document 1, it was necessary to appropriately determine a range (fit window) necessary and sufficient to approximate the strain distribution inside the necking for each material.

[0016] Furthermore, the method of Non-Patent Document 1 has the problem that the approximated strain distribution is strongly affected by experimental errors. In particular, in high-strength steel sheets with a significantly small work hardening rate, in addition to the strain peak leading to fracture, secondary and tertiary peaks may occur near the fractured area, as illustrated in Figure 12. Even if the forming limit strain is obtained by approximating the strain distribution in a state where such secondary peaks occur, the accuracy is reduced due to the influence of the secondary peaks. Therefore, when attempting to approximate the strain without the influence of the secondary peaks, it is difficult to determine an appropriate range (fit window) for approximating the strain distribution.

[0017] Furthermore, the method of Non-Patent Document 2 determines the forming limit from the time change in strain at the fracture initiation site of the test specimen, and is therefore less susceptible to the influence of the vicinity of the fracture initiation site than the method of Non-Patent Document 1, and is able to determine the forming limit with higher accuracy. However, the forming limit determined by the method of Non-Patent Document 2 is often greater than the necking limit, at which it is determined that the actual press-formed product cannot be formed in the manufacturing process. Therefore, it has sometimes been difficult to use this method for predicting the press formability of actual press-formed products.

[0018] The present invention has been made to solve the above problems, and an object of the present invention is to provide a method for determining the forming limit of a metal plate, a system for determining the forming limit of a metal plate, and a program for determining the forming limit of a metal plate, which are capable of accurately determining the forming limit in a forming test using a metal plate test piece. [Means for solving the problem]

[0019] The inventors have conducted extensive research into methods for solving the problems inherent in conventional techniques for determining the forming limit of metal sheets. In the research, the inventors focused on visual and tactile confirmation of necking 105 occurring in a test piece 101, as shown in FIG.

[0020] The constriction 105 can be visually confirmed by (i) the shadows created by shining a light 111 on the surface of the test piece 101, and (ii) the unevenness of gloss created by sanding the surface of the test piece 101, as shown in Figure 13(b). Furthermore, confirmation of the constriction by touch is performed by touching the surface of the test piece 101 with a finger to determine whether or not a constriction 105 is present, as shown in FIG. 13(c).

[0021] The presence or absence of necking 105, both visually and by touch, is recognized by the surface shape of test piece 101. The inventors therefore considered that it might be possible to evaluate the presence or absence of necking 105 by examining changes in the surface shape of test piece 101, and determine the forming limit. Furthermore, if necking 105 can be evaluated based on changes in the surface shape of test piece 101, it becomes possible to directly measure the strain inside necking 105 without approximation. Therefore, it has been discovered that this method can solve problems such as the fact that, as in conventional methods, the strain distribution changes depending on the material properties (n value) of the metal plate, and that the distribution of strain occurring on the surface of test piece 101 cannot be appropriately approximated due to secondary and tertiary peaks seen in the strain distribution of high-strength steel plate, making it impossible to accurately determine the strain that is the forming limit. The present invention has been completed based on this finding, and specifically has the following configuration.

[0022] (1) The forming limit determination method for a metal sheet according to the present invention determines the forming limit of a metal sheet, The method includes a forming test step, a forming limit analysis step, and a forming limit determination step, The molding test step includes: a test piece preparation step of preparing a test piece having a predetermined grid or strain analysis pattern on the surface of the metal plate; a test piece molding step of molding the test piece while sequentially photographing the surface of the test piece having the lattice or strain analysis pattern attached thereto; a strain and three-dimensional coordinate measuring step of analyzing images sequentially taken in the test piece molding step and measuring the strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; a database construction step of storing the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture to construct a database, The forming limit analysis step includes: a fracture orthogonal direction specifying step of specifying a fracture orthogonal direction that is orthogonal to a fracture portion generated in the test piece; an evaluation point sequence setting step of setting an evaluation point sequence on the test piece to acquire the distribution of strain or three-dimensional coordinates at the fractured portion and its vicinity in the fracture orthogonal direction; a strain or three-dimensional coordinate extraction step of extracting from the database strain or three-dimensional coordinates in the evaluation point sequence at a predetermined forming step of the test piece, The forming limit determination step a fracture orthogonal direction gradient calculation step of calculating a fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted in the strain or three-dimensional coordinate extraction step; and a forming limit determination step of determining the forming limit of the test piece based on the calculated strain or the fracture orthogonal direction gradient of the three-dimensional coordinates.

[0023] (2) In the above (1), The method is characterized in that in the fracture orthogonal direction gradient calculation step, a fracture orthogonal direction gradient of the plate thickness direction strain in the evaluation point sequence is calculated.

[0024] (3) In the above (1), In the fracture orthogonal direction gradient calculation step, the three-dimensional coordinates in the evaluation point sequence are converted into normal direction coordinates and tangential direction coordinates of the surface of the test piece, and the tangential direction gradient of the normal direction coordinates is calculated as the fracture orthogonal direction gradient of the three-dimensional coordinates.

[0025] (4) In the above (1), In the forming limit determination process, it is determined that necking has occurred in a forming step in which the strain in the evaluation point sequence or the gradient in the fracture orthogonal direction of the three-dimensional coordinates exceeds a predetermined threshold value, and the strain in the fracture portion in the forming step immediately before which it was determined that necking has occurred is taken as the forming limit strain.

[0026] (5) In any one of (1) to (4) above, In the molding test step, a plurality of test pieces having different shapes are prepared and molded; In the forming limit analysis step, strains and three-dimensional coordinates in the evaluation point sequence are extracted for each of the plurality of test specimens; In the forming limit determining step, the forming limit is determined for each of the plurality of test pieces to obtain a forming limit line.

[0027] (6) The forming limit determination system for a metal sheet according to the present invention determines the forming limit of a metal sheet, The apparatus includes a forming test device, a forming limit analysis device, and a forming limit determination device, The forming test device a forming die for forming a test piece of the metal plate having a predetermined grid or strain analysis pattern on its surface; an imaging device that sequentially images the surface of the test piece during the molding process of the test piece by the molding die; a strain and three-dimensional coordinate measuring device that analyzes images of the surface of the test piece sequentially photographed by the photographing device and measures the strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; a database construction device that stores the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture and constructs a database, The forming limit analysis device is a fracture orthogonal direction specifying unit that specifies a fracture orthogonal direction that is orthogonal to a fracture portion that occurs in the test piece molded by the molding test device; an evaluation point sequence setting unit that sets an evaluation point sequence on the test piece to acquire a distribution of strain or three-dimensional coordinates at the fractured portion and its vicinity in the fracture orthogonal direction; a strain or three-dimensional coordinate extraction unit that extracts strain or three-dimensional coordinates in an evaluation point sequence at a predetermined forming step of the test piece from the database; The forming limit determination device is a fracture orthogonal direction gradient calculation unit that calculates a fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted by the strain or three-dimensional coordinate extraction unit; and a forming limit determination unit that determines the forming limit of the test piece based on the calculated strain or the gradient of the three-dimensional coordinates in the direction perpendicular to fracture.

[0028] (7) In the above (6), The forming limit determination device is characterized in that it calculates a gradient of the thickness direction strain in the evaluation point sequence in a direction perpendicular to fracture and determines the forming limit of the test piece.

[0029] (8) In the above (6), The forming limit determination device is characterized in that it converts three-dimensional coordinates in the evaluation point sequence into normal coordinates and tangential coordinates of the test piece, and calculates the gradient of the normal coordinates in the fracture orthogonal direction as the fracture orthogonal direction gradient of the three-dimensional coordinates.

[0030] (9) In the above (6), The forming limit determination device is characterized in that it determines that necking has occurred in a forming step in which the strain in the evaluation point sequence or the gradient in the fracture orthogonal direction of the three-dimensional coordinates exceeds a predetermined threshold, and determines the strain in the fracture portion in the forming step immediately before which it is determined that necking has occurred as the forming limit strain.

[0031] (10) In any one of (6) to (9) above, The molding test device molds a plurality of test pieces having different shapes, the forming limit analysis device extracts strain and three-dimensional coordinates in the evaluation point sequence for each of the plurality of test pieces; The forming limit determining device is characterized in that it determines the forming limit for each of the plurality of test pieces and obtains a forming limit line.

[0032] (11) A forming limit determination program for a metal sheet according to the present invention is for determining the forming limit of a metal sheet, The forming limit determination system for a metal sheet according to any one of (5) to (10) above has a function of causing a computer to function as the forming limit analysis device and the forming limit determination device. [Effects of the Invention]

[0033] According to the present invention, by calculating the strain or the gradient of three-dimensional coordinates on the surface of a metal plate test piece in the direction perpendicular to the fracture, it is possible to determine whether or not necking has occurred based on changes in the surface shape of the test piece, thereby making it possible to accurately determine the forming limit of the metal plate. Furthermore, according to the present invention, the forming limit of a metal sheet can be determined by eliminating the influence of strain distribution due to material properties such as the material strength and work hardening rate of the metal sheet. [Brief explanation of the drawings]

[0034] [Figure 1] FIG. 1 is a flowchart showing a process flow of a forming limit determination method for a metal sheet according to an embodiment of the present invention. [Figure 2] FIG. 2 is a diagram showing the shape of a metal plate test piece used in a stretch test in the embodiments and examples of the present invention. [Figure 3] 1 is a diagram showing an example of a forming die used to form a test piece in a forming limit determination method and forming limit determination device for a metal plate according to an embodiment of the present invention. FIG. [Figure 4] FIG. 2 is a diagram showing a fracture orthogonal direction perpendicular to a fracture portion generated in a formed test piece in a forming limit determination method for a metal sheet according to an embodiment of the present invention. [Figure 5] 1 is a graph illustrating a gradient of strain in a direction perpendicular to fracture, which is related to determining the forming limit of a test specimen, in the forming limit determination method according to an embodiment of the present invention. [Figure 6] 1 is a diagram showing a configuration of a forming limit determination system for a metal sheet according to an embodiment of the present invention; [Figure 7-1] 1 is a graph showing the distribution of maximum principal strain on the surface of a molded test piece in an example ((a) molding step: 300 steps, (b) molding step: 500 steps, (c) molding step: 800 steps). [Figure 7-2] 10 is a graph showing the distribution of maximum principal strain on the surface of a molded test piece in an example ((d) molding step: 1000 steps, (e) molding step: 1100 steps, (f) molding step: 1160 steps). [Figure 7-3] 1 is a graph showing the distribution of maximum principal strain on the surface of a molded test piece in an example ((g) molding step: 1180 steps, (h) molding step: 1200 steps, (i) molding step: 1210 steps). [Figure 8-1] Graphs showing the distribution of strain in the thickness direction and its gradient perpendicular to the fracture direction on the surface of molded test pieces in the examples ((a) molding step: 300 steps, (b) molding step: 500 steps, (c) molding step: 800 steps). [Figure 8-2] In the examples, this is a graph showing the distribution of the thickness direction strain and its gradient in the direction perpendicular to the fracture on the surface of the formed test piece ((d) forming step: 1000 steps, (e) forming step: 1100 steps, (f) forming step: 1160 steps). [Figure 8-3] This is a graph showing the distribution of the thickness direction strain and its gradient in the direction perpendicular to the fracture on the surface of a molded test piece in the example ((g) molding step: 1180 steps, (h) molding step: 1200 steps, (i) molding step: 1210 steps). [Figure 9] 1 is a graph showing the transition of the necking ratio over the course of a test piece in an example. [Figure 10] FIG. 2 is a forming limit diagram obtained in the examples. [Figure 11]FIG. 1 shows the Nakajima method and the Marciniak method, which are conventional methods for determining the forming limit of metal sheets, and examples of forming limit diagrams determined by these methods ((a) Nakajima method, (b) Marciniak method, (c) forming limit diagrams determined by both the Nakajima method and the Marciniak method). [Figure 12] 1 is a graph showing an example of the distribution of strain generated on the surface of a metal plate. [Figure 13] 1A and 1B are diagrams explaining how to check for necking in a metal plate during a forming test ((a) cross-sectional view of necking in a metal plate, (b) visual confirmation of necking, (c) confirmation by touch). DETAILED DESCRIPTION OF THE INVENTION

[0035] <Method for determining the forming limit of metal sheets> The method for determining the forming limit of a metal sheet according to this embodiment determines the forming limit of a metal sheet, and as shown in FIG. 1, includes a forming test step S10, a forming limit analysis step S20, and a forming limit determination step S30.

[0036] <Molding test stage> As shown in FIG. 1, the forming test stage S10 includes a test piece preparation step S11, a test piece forming step S13, a strain and three-dimensional coordinate measurement step S15, and a database construction step S17.

[0037] (Test piece preparation process) The test piece preparation step S11 is a step of preparing a test piece in which a predetermined grid or strain analysis pattern is applied to the surface of a metal plate.

[0038] Figure 2 shows a specific example of a test piece 101. Figure 2(a) shows a disk-shaped test piece 101, and Figures 2(b) and 2(c) show test pieces 101 in which arc-shaped cutout portions 101a are formed at diametrically opposing positions on the peripheral edge of the disk, and the widths W of central portions 101b are different.

[0039] The strain analysis pattern applied to the surface of the test piece 101 may be, for example, an arrangement of circles or dots. The lattice or strain analysis pattern may be a regular repeating pattern or an irregular random pattern. To provide a grid or a pattern for strain analysis, for example, a sample grid may be transferred onto the surface of the test piece 101 .

[0040] (Test piece molding process) The test piece forming step S13 is a step of forming the test piece 101 while sequentially photographing the surface of the test piece 101 to which the grid or strain analysis pattern has been applied in the test piece preparation step S11.

[0041] In the test piece molding step S13, the test piece 101 is bulged using a molding die 11 equipped with a punch 11a, an upper die 11b, and a blank holder 11c, as shown in FIG. The bulging of the test piece 101 in the test piece molding step S13 is not limited to using a spherical-headed punch 11a as shown in Figure 3, but may also use a flat-headed punch 213 with a flat tip 213a as shown in Figure 11(b) described above.

[0042] In addition, the sequential photographing of the surface of the test piece 101 is performed by using two cameras to photograph the surface of the test piece 101 during the molding process at predetermined time intervals, and images of the surface of the test piece 101 during each molding step are obtained. Note that a molding step refers to a time step in which the surface of the test piece 101 is sequentially photographed at predetermined time intervals during the molding process of the test piece 101.

[0043] (Strain and 3D coordinate measurement process) The strain and three-dimensional coordinate measuring step S15 is a step of analyzing the images sequentially taken in the test piece molding step S13, and measuring the strain occurring on the surface of the test piece 101 and the three-dimensional coordinates of the surface.

[0044] The measurement of the strain and three-dimensional coordinates on the surface of the test piece 101 is preferably performed by digital image correlation (DIC). DIC can measure the strain in two in-plane directions on the surface of the test piece 101 and the three-dimensional coordinates of the surface (surface shape of the test piece 101) from the deformation state of a grid or strain analysis pattern attached to the surface of the test piece 101. Furthermore, DIC preferably measures the maximum principal strain and the minimum principal strain as the strain in two in-plane directions on the surface of the test piece 101.

[0045] (Database construction process) The database construction step S17 is a step of storing the strains and three-dimensional coordinates measured in the strain and three-dimensional coordinate measuring step S15 in chronological order from the start of forming to fracture to construct a database.

[0046] In this embodiment, after the strain and three-dimensional coordinates are stored in the database in the database construction step S17, it is determined whether or not fracture has occurred in the test piece 101 (S19). If it is determined that no fracture has occurred, the molding step is advanced, and the test piece molding step S13, the strain and three-dimensional coordinate measuring step S15, and the database construction step S17 are repeated. This is repeated until it is determined (S19) that a fracture has occurred in the test piece 101. This makes it possible to construct a database that stores the strain that occurs on the surface of the test piece 101 and the three-dimensional coordinates of the surface in each molding step from the start of molding to fracture.

[0047] <Forming limit analysis stage> As shown in FIG. 1, the forming limit analysis stage S20 includes a fracture orthogonal direction specifying step S21, an evaluation point sequence setting step S23, and a strain or three-dimensional coordinate extraction step S25.

[0048] (Fracture orthogonal direction identification process) The fracture orthogonal direction specifying step S21 is a step of specifying a fracture orthogonal direction that is orthogonal to the fractured portion 103 generated in the test piece 101 in the test piece molding step S13.

[0049] 4 is a schematic diagram showing (a) a fracture 103 that occurred in the test piece 101, and (b) a necking 105 that leads to the fracture 103 in the test piece 101. The necking 105 is a location where the sheet thickness is locally reduced in the AA cross section perpendicular to the fracture 103. The direction parallel to the fracture 103 is the fracture direction, and the direction perpendicular to the fracture 103 is the fracture orthogonal direction.

[0050] (Evaluation point sequence setting process) The evaluation point sequence setting step S23 is a step of setting an evaluation point sequence on the test piece 101 for acquiring the strain or three-dimensional coordinate distribution in the direction perpendicular to the fracture at the fractured portion 103 occurring in the test piece 101 and its vicinity. The evaluation point sequence may be set at predetermined intervals along the direction perpendicular to the fracture so as to straddle the fractured portion 103 in the test piece 101, for example.

[0051] (Strain or 3D coordinate extraction process) The strain or three-dimensional coordinate extraction process S25 is a process of extracting the strain or three-dimensional coordinates in the evaluation point sequence at a specified molding step of the test piece 101 molded in the test piece molding process S13 from the database constructed in the database construction process S17.

[0052] The specified molding step for extracting strain or three-dimensional coordinates from the database may be, for example, all time steps from the start of molding of the test piece 101 to fracture, or it may be a time step before or after the fracture occurs, and may be set as appropriate.

[0053] 1, the forming limit analysis step S20 according to this embodiment extracts strain or three-dimensional coordinates in the evaluation point sequence at a predetermined forming step (S25), and then determines whether or not fracture has occurred in the test piece 101 (S27). If it is determined that no fracture has occurred, the process proceeds to the forming step, and the extraction of strain or three-dimensional coordinates (S25) and the determination of whether or not fracture has occurred (S27) are repeated. This repetition is repeated until it is determined that fracture has occurred in the test piece 101 (S27). This makes it possible to extract strain or three-dimensional coordinates in the evaluation point sequence at each forming step until fracture occurs.

[0054] <Forming limit determination stage> As shown in FIG. 1, the forming limit determination step S30 includes a fracture orthogonal direction gradient calculation step S31 and a forming limit determination step S33.

[0055] (Fracture perpendicular direction gradient calculation process) The fracture orthogonal direction gradient calculation step S31 is a step of calculating the fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted in the strain or three-dimensional coordinate extraction step S25.

[0056] In the fracture orthogonal direction gradient calculation step S31 according to this embodiment, the fracture orthogonal direction gradient of the thickness direction strain ε is calculated as shown in Fig. 5. The thickness direction strain ε can be calculated from the strains in two in-plane directions measured by DIC and extracted from a database according to the law of constant volume.

[0057] Figure 5(a) shows the distribution of the transverse-to-fracture direction gradient of the thickness direction strain calculated in the transverse-to-fracture direction gradient calculation step S31, and Figure 5(b) shows the distribution of the transverse-to-fracture direction of the thickness direction strain. In Figures 5(a) and 5(b), x is the coordinate in the transverse-to-fracture direction of the evaluation point sequence, εz is the thickness direction strain, a is the transverse-to-fracture direction gradient of the thickness direction strain, and n is the nth evaluation point set along the transverse-to-fracture direction. The transverse-to-fracture direction gradient of the thickness direction strain can be calculated using the thickness direction strain of the nth and (n+1)th evaluation points and their coordinates, for example, as shown in Figure 5(b).

[0058] (Forming limit determination process) The forming limit determination step S33 is a step of determining the forming limit of the test piece 101 based on the strain or the fracture orthogonal direction gradient of the three-dimensional coordinates calculated in the fracture orthogonal direction gradient calculation step S31.

[0059] In this embodiment, the forming limit determination step S33 first determines, for each forming step, the maximum value of the fracture orthogonal direction gradient of the thickness direction strain in the evaluation point sequence calculated in the fracture orthogonal direction gradient calculation step S31. When necking occurs in the test piece 101, the change in the thickness direction strain becomes steeper and the fracture orthogonal direction gradient becomes larger. Therefore, when the maximum value of the fracture orthogonal direction gradient exceeds a predetermined threshold, it is determined that necking has occurred.

[0060] The strain gradient in the direction perpendicular to the fracture changes from negative to positive across the fracture (see FIG. 5(a)). When necking occurs in the test piece 101, the change in the thickness direction strain becomes steep even in the region where the strain gradient in the direction perpendicular to the fracture is negative. Therefore, in the forming limit determination step S33, it is advisable to find the maximum absolute value of the strain gradient in the direction perpendicular to the fracture.

[0061] The threshold value used to determine the occurrence of necking can be determined taking into consideration the material, the shape of the press-formed product, and its intended use. For example, samples having various gradients of thickness strain perpendicular to the fracture direction can be prepared, and the critical value of the gradient of thickness strain perpendicular to the fracture direction at which necking occurs can be determined by visual inspection or touch, and this critical value can be used as the threshold value.

[0062] In the above explanation, the reason why the gradient of the thickness direction strain in the direction perpendicular to the fracture is used to determine the forming limit is that it can capture changes in the surface shape that occur in the test piece 101 during the forming test, and can accurately determine whether or not necking occurs.

[0063] However, the present invention may also use the surface shape of the test piece 101, that is, the three-dimensional coordinates of the surface of the test piece 101. In this case, first, the three-dimensional coordinates of the evaluation point sequence in a predetermined molding step of the test piece 101 molded in the test piece molding step S13 are extracted from the database constructed in the database construction step S17 (S25). Next, the gradient of the three-dimensional coordinates in the direction orthogonal to the fracture in the extracted evaluation point sequence is calculated (S31), and the forming limit of the test piece 101 is determined based on the calculated gradient of the three-dimensional coordinates in the direction orthogonal to the fracture (S33).

[0064] When determining the forming limit using the three-dimensional coordinates of the surface of the test piece 101, it is advisable to use the coordinates of the surface of the test piece 101 in the thickness direction. When necking occurs in the test piece 101 during the forming test, the change in the thickness direction coordinate becomes steeper, and the fracture orthogonal direction gradient becomes larger, similar to the thickness direction strain. Therefore, in the forming limit determination step S33, it can be determined that necking has occurred in the test piece 101 when the fracture orthogonal direction gradient of the thickness direction coordinate exceeds a predetermined threshold. The threshold for determining the occurrence of necking based on the thickness direction coordinate can be determined in the same way as for the thickness direction strain. Furthermore, the occurrence of necking can be determined using the maximum absolute value of the fracture orthogonal direction gradient of the thickness direction coordinate.

[0065] The thickness direction coordinates of the surface of the test piece 101 can be acquired or calculated from the three-dimensional coordinates of the surface of the test piece 101. For example, when forming the test piece 101 using a flat-head punch 213 as in the Marciniak method shown in Fig. 11(b), it is sufficient to measure the coordinates in two in-plane directions on the surface of the test piece 101 and the coordinate in the out-of-plane direction perpendicular to these directions as the three-dimensional coordinates of the surface of the test piece 101. In this case, of the measured three-dimensional coordinates, the coordinate in the out-of-plane direction can be obtained as the plate thickness direction coordinate.

[0066] On the other hand, when the test piece 101 is formed using a spherical punch 203 with a spherical tip 203a, as in the Nakajima method shown in Figure 11(a), the test piece 101 is bent and deformed, so the orientation of the thickness direction coordinate changes during the forming process, and the thickness direction coordinate cannot be obtained directly. In this case, in the forming limit determination step S30, the three-dimensional coordinates in the evaluation point sequence are transformed into normal coordinates and tangential coordinates on the surface of the test piece 101, the normal coordinates are set as plate thickness coordinates, and the tangential direction is set to coincide with the fracture orthogonal direction. This makes it possible to calculate the tangential gradient of the transformed normal coordinates as the fracture orthogonal direction gradient of the plate thickness coordinates.

[0067] In the method for determining the forming limit of a metal sheet according to this embodiment, first, in a forming test step S10, multiple test pieces 101 with different shapes are formed, and the strain and three-dimensional coordinates are measured. Subsequently, in a forming limit analysis step S20, the strain and three-dimensional coordinates of the evaluation point sequence are extracted for each of the multiple test pieces 101. Furthermore, in a forming limit determination step S30, the forming limit is determined for each of the multiple test pieces 101, and the forming limit strain is calculated. The strain at the fractured portion in the forming step immediately prior to the forming step in which necking is determined to have occurred is calculated as the forming limit strain. This allows a forming limit diagram of the metal sheet to be obtained. The forming limit strain may be, for example, the strain at the fractured portion in the forming step immediately prior to the forming step in which necking is determined to have occurred.

[0068] <Metal sheet forming limit judgment system> The forming limit determination system 1 for a metal plate according to this embodiment (hereinafter referred to as "the forming limit determination system 1") determines the forming limit of a metal plate, and as shown in FIG. 6, includes a forming test device 10, a forming limit analysis device 20, and a forming limit determination device 30.

[0069] <Forming test equipment> The forming test device 10 includes a forming mold 11 , a photographing device 13 , a strain and three-dimensional coordinate measuring device 15 , and a database creating device 17 .

[0070] (Molding mold) The forming die 11 is used to form a metal plate test piece 101 having a predetermined lattice or strain analysis pattern on its surface. As shown in Fig. 3, the forming die 11 can be exemplified by one including a punch 11a, an upper die 11b, and a blank holder 11c.

[0071] (imaging device) The photographing device 13 sequentially photographs the surface of the test piece 101 during the process of molding the test piece 101 using the molding die 11. As the photographing device 13, for example, one composed of two cameras and capable of stereoscopically photographing the surface of the test piece 101 can be mentioned.

[0072] (Strain and 3D coordinate measuring device) The strain and three-dimensional coordinate measuring device 15 analyzes images of the surface of the test piece 101 sequentially photographed by the photographing device 13, and measures the strain occurring on the surface of the test piece 101 and the three-dimensional coordinates of the surface.

[0073] (Database construction device) The database construction device 17 is a device that stores the strain and three-dimensional coordinates measured by the strain and three-dimensional coordinate measuring device 15 in chronological order from the start of forming to fracture, and constructs a database.

[0074] <Forming limit analysis device> The forming limit analysis device 20 includes a fracture orthogonal direction specifying unit 21 , an evaluation point sequence setting unit 23 , and a strain or three-dimensional coordinate extracting unit 25 . The forming limit analysis device 20 can be, for example, configured by a computer (such as a PC). In this case, each unit of the forming limit analysis device 20 functions when the CPU of the computer executes a predetermined program.

[0075] (Fracture orthogonal direction identification part) The fracture orthogonal direction specifying unit 21 specifies a fracture orthogonal direction that is orthogonal to a fracture 103 that occurs in the test piece 101 formed by the forming test device 10. (Evaluation score sequence setting section) The evaluation point sequence setting unit 23 sets a sequence of evaluation points on the test piece 101 for acquiring the distribution of strain and three-dimensional coordinates in the vicinity of the fractured portion 103 .

[0076] (Strain or 3D coordinate extraction section) The strain or three-dimensional coordinate extraction unit 25 extracts the strain or three-dimensional coordinate of the evaluation point sequence in a predetermined forming step of the test piece 101 from the database.

[0077] <Forming limit judgment device> The forming limit determination device 30 includes a fracture orthogonal direction gradient calculation unit 31 and a forming limit determination unit 33 . The forming limit determining device 30 can be, for example, configured by a computer (such as a PC). In this case, each part of the forming limit determining device 30 functions when the CPU of the computer executes a predetermined program.

[0078] (Fracture perpendicular direction gradient calculation section) The fracture orthogonal direction gradient calculation unit 31 calculates the fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted by the strain or three-dimensional coordinate extraction unit 25.

[0079] (Forming limit judgment section) The forming limit determination unit 33 determines the forming limit of the test piece 101 based on the strain or the fracture orthogonal direction gradient of the three-dimensional coordinates in the calculated evaluation point sequence.

[0080] The forming limit determination device 30 may calculate the fracture orthogonal direction gradient of the thickness direction strain in the evaluation point sequence by the fracture orthogonal direction gradient calculation unit 31, or may calculate the fracture orthogonal direction gradient of the three-dimensional coordinates in the evaluation point sequence.

[0081] When calculating the fracture orthogonal direction gradient of the three-dimensional coordinates in the evaluation point sequence, the forming limit determination device 30 may calculate the fracture orthogonal direction gradient of the plate thickness direction coordinates on the surface of the test piece 101 as the three-dimensional coordinates.

[0082] Furthermore, when the test piece 101 is bent as in the Nakajima method (FIG. 11(a)), as described above, the forming limit determination device 30 first converts the three-dimensional coordinates in the evaluation point sequence into normal coordinates and tangential coordinates of the surface of the test piece 101. Then, the forming limit determination device 30 may calculate the gradient of the normal coordinates in the tangential direction as the gradient of the three-dimensional coordinates (plate thickness direction coordinates) in the fracture orthogonal direction.

[0083] Furthermore, the forming limit determination device 30 determines, by the forming limit determination unit 33, that necking has occurred in a forming step where the strain in the evaluation point sequence or the fracture orthogonal direction gradient of the three-dimensional coordinates exceeds a predetermined threshold value.

[0084] The forming limit determination system 1 according to this embodiment can obtain the forming limit line of a metal plate. To this end, the forming test apparatus 10 forms a plurality of test pieces with different shapes, and the forming limit analysis apparatus 20 extracts the strain and three-dimensional coordinates in the evaluation point sequence for each of the plurality of test pieces formed by the forming test apparatus 10. Furthermore, the forming limit determination apparatus 30 determines the forming limit for each of the plurality of test pieces and determines the forming limit strain. This allows the forming limit determination system 1 to obtain a forming limit line using the forming limit strains determined for the plurality of test pieces 101. Note that the forming limit strain may be, for example, the strain at the fractured portion in the forming step immediately before it is determined that necking has occurred.

[0085] <Forming limit judgment program for metal sheets> The embodiment of the present invention can be configured as a forming limit judgment program for metal sheets that causes the forming limit analysis device 20 and the forming limit judgment device 30 configured by a computer to function.

[0086] That is, the forming limit judgment program for a metal sheet according to the present embodiment judges the forming limit of a metal sheet, and has a function of causing a computer to execute the forming limit analysis device 20 and the forming limit judgment device 30 shown in FIG. 6.

[0087] The forming limit determination program for metal plates according to this embodiment causes the forming limit analysis device 20 to function as a fracture orthogonal direction identification unit 21, an evaluation point sequence setting unit 23, and a strain or three-dimensional coordinate extraction unit 25.

[0088] Furthermore, the forming limit judgment program for a metal sheet according to this embodiment causes the forming limit judgment device 30 to function as a fracture orthogonal direction gradient calculation unit 31 and a forming limit judgment unit 33.

[0089] As described above, in the method for determining the forming limit of a metal sheet, the system for determining the forming limit of a metal sheet, and the program for determining the forming limit of a metal sheet according to the present embodiment, the strain on the surface of the test piece or the gradient of the three-dimensional coordinates in the direction perpendicular to the fracture is calculated. This makes it possible to determine the occurrence of necking based on the change in the surface shape of the test piece, thereby making it possible to determine the forming limit of the metal sheet with high accuracy. Furthermore, according to the method for determining the forming limit of a metal plate, the system for determining the forming limit of a metal plate, and the program for determining the forming limit of a metal plate according to the present embodiment, it is possible to determine the forming limit of a metal plate while eliminating the influence of strain distribution due to material properties such as the material strength and work hardening rate of the metal plate. [Example]

[0090] An experiment was conducted to verify the effects of the present invention, and the results will be described below.

[0091] In the experiment, the method for determining the forming limit of a metal sheet according to the present embodiment described above was carried out, and the forming of the metal sheet, and the analysis and determination of the forming limit were carried out. The metal plate used was a high-strength steel plate with a tensile strength of 590 MPa and a thickness of 1.6 mm. As shown in Figures 2(b) and 2(c) above, test pieces 101 were prepared, each having a circular plate shape with a diameter of 100 mm, with arc-shaped cutouts 101a formed at diametrically opposed positions on the periphery, and the width W of the central portion 101b was set to 32 mm or 48 mm.

[0092] A hydraulic deep drawing test machine equipped with a forming die 11 consisting of a round-headed punch 11a with a radius of 25 mm, an upper die 11b, and a blank holder 11c was used to form the test piece 101. A blank holder force of 980 kN was applied to the blank holder 11c to prevent the test piece 101 from flowing in during forming, and the punch speed was set to 5 mm / min. Then, two cameras for image analysis installed above the molding die 11 successively photographed the surface of the test piece 101 at intervals of once per second from the start of molding until fracture occurred.

[0093] Next, the images of the surface of the test piece 101 taken sequentially were subjected to image analysis, and the strain (maximum principal strain and minimum principal strain) generated on the surface of the test piece 101 and the three-dimensional coordinates of the surface were measured. The strain and three-dimensional coordinates were measured at each forming step, in which the test piece 101 was photographed sequentially from the start of forming to fracture, and the measured strain and three-dimensional coordinates were stored in chronological order to construct a database.

[0094] 7-1 to 7-3 are graphs showing the distribution of maximum principal strains on the surface of the test piece 101 measured in each forming step as an example of the measured strain. As shown in FIGS. 7-1 to 7-3, as the forming steps progress, the strain generated on the surface of the test piece 101 increases and spreads around the fractured area. Then, in forming step 1210, a fractured area occurred in the test piece 101.

[0095] Next, as shown in Figure 7-3, the fracture orthogonal direction perpendicular to the fracture occurring in the test piece 101 was identified, and an evaluation point sequence was set on the test piece 101 to obtain the strain and three-dimensional coordinate distribution near the fracture. Then, the strain in the evaluation point sequence was extracted from the database of strain and three-dimensional coordinate constructed by the forming test.

[0096] Next, the thickness direction strain was calculated from the strain at the extracted evaluation point sequence, and the gradient of the thickness direction strain in the direction perpendicular to the fracture direction was calculated. Then, the forming limit of the test piece 101 was determined based on the gradient of the thickness direction strain in the direction perpendicular to the fracture direction.

[0097] In this example, a threshold value for the gradient of the thickness direction strain in the direction perpendicular to the fracture, which is determined to be the forming limit, was determined in advance from the shape of the necking that occurred in the test piece 101. Then, for each forming step in which the test piece 101 was formed, the ratio (strain gradient ratio) of the gradient of the thickness direction strain in the direction perpendicular to the fracture to the threshold value was calculated for the evaluation point sequence. Furthermore, the necking ratio, which is the maximum value of the strain gradient ratio, was calculated for each forming step, and a forming step in which the necking ratio exceeded 1 was determined to be the forming limit.

[0098] Figures 8-1 to 8-3 show the thickness direction strain and its gradient in the direction perpendicular to the fracture direction at the evaluation point sequence in each forming step. In Figures 8-1 to 8-3, the horizontal axis represents the coordinate of the evaluation point sequence in the direction perpendicular to the fracture (the position of the evaluation point sequence), the first vertical axis represents the thickness direction strain, and the second vertical axis represents the necking ratio. In Figures 8-1 to 8-3, the solid plots represent the thickness direction strain, the open plots represent the strain gradient ratio, and 0 on the horizontal axis represents the center position of the fracture that occurred in test piece 101.

[0099] As shown in Figures 8-1 to 8-3, as the forming steps progress, the thickness direction strain increases in the negative direction around the fracture. This increases the strain gradient ratio, i.e., the value of the fracture-orthogonal gradient of the thickness direction strain. It can be seen that the strain gradient ratio reaches its maximum value of 1 in the forming step 1160 (see Figure 8-2(f)).

[0100] Fig. 9 shows the transition of the necking ratio from the start of forming to the fracture of the test piece 101. As shown in Fig. 9, it can be seen that the necking ratio increases as the forming steps progress, and exceeds 1 in forming step 1160. As such, from the results shown in Figs. 8-1 to 8-3 and 9, it was determined that the forming limit was reached in forming step 1160.

[0101] Furthermore, in the examples, forming tests were carried out using a plurality of test pieces 101 in which the shape of the notch 101a was changed, and the forming limit was determined to find the forming limit strain. Table 1 shows the forming limit strains obtained using a plurality of test pieces 101 with different shapes. Furthermore, Fig. 10 shows the forming limit lines obtained using a plurality of test pieces 101 with different shapes. [Table 1]

[0102] As described above, it has been demonstrated that the present invention enables the accurate determination of the forming limit of a metal sheet from the shape of the necking that occurs in a formed test piece. Furthermore, it has been demonstrated that the present invention enables the determination of the forming limit for a plurality of test pieces with different shapes and the determination of the forming limit strain, thereby obtaining a forming limit line. [Explanation of symbols]

[0103] 1. Forming limit judgment system 10. Forming test equipment 11 Molding mold 11a Punch 11b Upper die 11c Wrinkle holder 13 Imaging equipment 15 Strain and 3D coordinate measuring device 17 Database construction device 20 Forming limit analysis equipment 21 Fracture orthogonal direction identification section 23 Evaluation point sequence setting section 25 Strain or 3D coordinate extraction unit 30 Forming limit determination device 31 Calculation of gradient in the direction perpendicular to fracture 33 Forming Limit Judgment Section 101 Test piece 101a Notch 101b Central part 103 Breaking part 105 Waist 107 File section 111 Light 201 Molding mold 203 Ball Head Punch 203a Tip 205 Upper die 207 Wrinkle holder 211 Molding mold 213 Flat Head Punch 213a Tip 215 driving seat

Claims

1. A method for determining a forming limit of a metal plate, comprising: The method includes a forming test step, a forming limit analysis step, and a forming limit determination step, The molding test step includes: a test piece preparation step of preparing a test piece having a predetermined grid or strain analysis pattern on the surface of the metal plate; a test piece molding step of molding the test piece while sequentially photographing the surface of the test piece having the lattice or strain analysis pattern attached thereto; a strain and three-dimensional coordinate measuring step of analyzing images sequentially taken in the test piece molding step and measuring the strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; a database construction step of storing the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture to construct a database, The forming limit analysis step includes: a fracture orthogonal direction specifying step of specifying a fracture orthogonal direction that is orthogonal to a fracture portion generated in the test piece; an evaluation point sequence setting step of setting an evaluation point sequence on the test piece to acquire a distribution of strain or three-dimensional coordinates at the fractured portion and its vicinity in the fracture orthogonal direction; a strain or three-dimensional coordinate extraction step of extracting from the database strain or three-dimensional coordinates in the evaluation point sequence at a predetermined forming step of the test piece, The forming limit determination step a fracture orthogonal direction gradient calculation step of calculating a fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted in the strain or three-dimensional coordinate extraction step; and a forming limit determination step of determining the forming limit of the test piece based on the calculated strain or the fracture orthogonal direction gradient of the three-dimensional coordinates.

2. 2. The method for determining the forming limit of a metal sheet according to claim 1, wherein the step of calculating the gradient in the direction perpendicular to the fracture comprises calculating a gradient in the direction perpendicular to the fracture of a thickness direction strain in the series of evaluation points.

3. 2. The method for determining the forming limit of a metal plate according to claim 1, wherein in the fracture orthogonal direction gradient calculation step, three-dimensional coordinates in the evaluation point sequence are transformed into normal direction coordinates and tangential direction coordinates of the surface of the test piece, and the tangential direction gradient of the normal direction coordinates is calculated as the fracture orthogonal direction gradient of the three-dimensional coordinates.

4. 4. The method for determining the forming limit of a metal sheet according to claim 1, wherein, in the forming limit determination step, it is determined that necking has occurred in a forming step in which the strain in the evaluation point sequence or the gradient in the fracture orthogonal direction of the three-dimensional coordinates exceeds a predetermined threshold value, and the strain in the fracture portion in the forming step immediately before which it is determined that necking has occurred is taken as the forming limit strain.

5. In the molding test step, a plurality of test pieces having different shapes are prepared and molded; In the forming limit analysis step, strains and three-dimensional coordinates in the evaluation point sequence are extracted for each of the plurality of test specimens; 5. The method for determining a forming limit of a metal plate according to claim 4, wherein, in the forming limit determining step, the forming limit is determined for each of the plurality of test pieces to obtain a forming limit line.

6. A metal plate forming limit determination system for determining a forming limit of a metal plate, The apparatus includes a forming test device, a forming limit analysis device, and a forming limit determination device, The forming test device a forming die for forming a test piece of the metal plate having a predetermined grid or strain analysis pattern on its surface; an imaging device that sequentially images the surface of the test piece during the molding process of the test piece by the molding die; a strain and three-dimensional coordinate measuring device that analyzes images of the surface of the test piece sequentially photographed by the photographing device and measures the strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; a database construction device that stores the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture and constructs a database; The forming limit analysis device is a fracture orthogonal direction specifying unit that specifies a fracture orthogonal direction that is orthogonal to a fracture portion that occurs in the test piece molded by the molding test device; an evaluation point sequence setting unit that sets an evaluation point sequence on the test piece to acquire a distribution of strain or three-dimensional coordinates at the fractured portion and its vicinity in the fracture orthogonal direction; a strain or three-dimensional coordinate extraction unit that extracts strain or three-dimensional coordinates in an evaluation point sequence in a predetermined forming step of the test piece from the database, The forming limit determination device is a fracture orthogonal direction gradient calculation unit that calculates a fracture orthogonal direction gradient of the strain or three-dimensional coordinates in the evaluation point sequence extracted by the strain or three-dimensional coordinate extraction unit; and a forming limit determination unit that determines the forming limit of the test piece based on the calculated strain or the fracture orthogonal direction gradient of the three-dimensional coordinates.

7. 7. The system for determining a forming limit of a metal sheet according to claim 6, wherein the forming limit determination device calculates a gradient of a thickness direction strain in the evaluation point sequence in a direction perpendicular to fracture, and determines the forming limit of the test piece.

8. 7. The forming limit judgment system for a metal plate according to claim 6, wherein the forming limit judgment device converts three-dimensional coordinates in the evaluation point sequence into normal direction coordinates and tangential direction coordinates of the test specimen, and calculates a gradient of the normal direction coordinates in the fracture orthogonal direction as a fracture orthogonal direction gradient of the three-dimensional coordinates.

9. 9. The system for determining forming limits of a metal sheet according to claim 6, wherein the forming limit determination device determines that necking has occurred in a forming step in which the strain in the evaluation point sequence or the gradient in the fracture orthogonal direction of the three-dimensional coordinates exceeds a predetermined threshold, and determines the strain in the fracture portion in the forming step immediately before which it has been determined that necking has occurred as the forming limit strain.

10. The molding test device molds a plurality of test pieces having different shapes, the forming limit analysis device extracts strain and three-dimensional coordinates in the evaluation point sequence for each of the plurality of test pieces; 10. The system for determining a forming limit of a metal plate according to claim 9, wherein the forming limit determination device determines a forming limit for each of the plurality of test pieces and obtains a forming limit line.

11. A forming limit determination program for determining a forming limit of a metal plate, 9. A forming limit judgment program for a metal sheet, comprising a function of causing a computer to execute the forming limit judgment system for a metal sheet according to claim 6 as a forming limit analyzer and a forming limit judgment device.

12. A forming limit determination program for determining a forming limit of a metal plate, 10. A forming limit judgment program for a metal sheet, comprising a function of causing a computer to execute the forming limit judgment system for a metal sheet according to claim 9 as a forming limit analyzer and a forming limit judgment device.

13. A forming limit determination program for determining a forming limit of a metal plate, 11. A forming limit determination program for a metal sheet, comprising a function of causing a computer to execute the forming limit determination system for a metal sheet according to claim 10 as a forming limit analyzer and a forming limit determination device.

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