Metal plate molding limit determination method, metal plate molding limit determination system, and metal plate molding limit determination program

Abstract

In a metal plate molding limit determination method according to the present invention: a surface of a test piece 101 is molded while being sequentially images, and a strain on the surface of the test piece 101, which is generated from the start of molding to a point at which fracture occurs, as well as three-dimensional coordinates of the surface of the test piece 101, are measured to construct a database (S10); an evaluation point string is set along a fracture orthogonal direction that is orthogonal to a fractured section 103 generated in the test piece 101, and strain or three-dimensional coordinates in the evaluation point string are extracted from the database (S20); and a fracture orthogonal direction gradient of the strain or the three-dimensional coordinates in the evaluation point string is calculated, and a molding limit is determined (S30).

Description

METHOD FOR DETERMINING FORMING LIMITS OF METAL PLATES, SYSTEM FOR DETERMINING FORMING LIMITS OF METAL PLATES, AND PROGRAM FOR DETERMINING FORMING LIMITS OF METAL PLATES

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

[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 material properties, such as the ductility of the metal sheet used as the material. In recent years, demand for lighter car bodies has led to efforts 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 production 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 commonly used to determine the forming limits of sheet metals. Forming limit diagrams are created by measuring the forming limits of various deformation types of sheet metals in press forming, such as equibiaxial deformation, non-equibiaxial deformation, plane strain deformation, and uniaxial deformation, through laboratory-scale forming tests. To create a FLD, the width of the test specimen is varied at several levels, and the strain ratio between the major and minor axes of the test specimen is changed, thereby measuring the strains in both the major and minor axes at the time of fracture.

[0005] In general, in sheet metal forming tests, a sheet metal specimen undergoes uniform deformation, followed by a process in which strain concentrates at specific locations on the specimen. During this process, a reduction in sheet thickness, called necking, occurs at the strain concentration point. After this reduction in sheet thickness, the sheet metal fractures. In press forming, necking can result in a defective product even if it does not result in fracture. Therefore, the forming limit of a sheet metal 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 approximately 10%, followed by fracture immediately thereafter. Therefore, the forming limit of high-strength steel sheets must be determined accurately, and several techniques have been proposed to achieve this.

[0006] Non-Patent Document 1 describes a method for identifying a forming limit curve. 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.

[0007] However, the method of Non-Patent Document 1 does not directly measure the forming limit strain, and therefore cannot adequately approximate the strain at the fracture initiation point, and there are cases where the forming limit strain cannot be determined. 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 continuously measures the strain occurring in a test piece during forming, and determines the forming limit strain from the change in strain at the fracture initiation point over time.

[0008] ISO 12004-2:2008, Metallic materials - Sheet and strip - Determination of forming-limit curves, 2008. 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).

[0009] As shown in Fig. 11 , Non-Patent Document 1 describes the Nakajima test and the Marciniak test (Marciniak punch stretching geometry) as methods for determining the forming limit by a stretch test of a test piece 101. The Nakajima test involves stretch-forming the test piece 101 using a forming die 201 equipped with a hemispherical punch 203 having a spherical head tip 203 a, an upper die 205, and a blank holder 207, as shown in Fig. 11 (a). On the other hand, the Marciniak method, as shown in FIG. 11( b ), uses a molding die 211 equipped with a flat punch 213 having a flat tip 213 a, an upper die 205, and a blank holder 207, and sandwiches a driving sheet / sliding sheet 215 between the flat punch 213 and the test piece 101 to bulge-mold 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 obtained 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 determined by the Nakajima method generally has a strain just before the occurrence of necking that is about 1 to 2% larger, as shown in Fig. 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 by 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 by press forming analysis based on 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 varies depending on the work hardening rate (n value) of the material. Therefore, in order to determine the forming limit using the method of 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 a problem in 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 portion, as illustrated in FIG. 12 . Even if the forming limit strain is calculated 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 of strain at the fracture initiation site of the test specimen, and therefore is less affected by the vicinity of the fracture initiation site than the method of Non-Patent Document 1, and can 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 for predicting the press formability of actual press-formed products.

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

[0019] The inventors have conducted extensive research into methods for solving the problems associated with 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] As shown in Fig. 13(b), the presence of the necking 105 is confirmed visually by (i) shading produced by shining a light 111 on the surface of the test piece 101, or (ii) uneven gloss produced by sanding / filing the surface of the test piece 101. The presence of the necking is confirmed by the sense of touch, as shown in Fig. 13(c), by touching the surface of the test piece 101 with a finger to determine whether or not the necking 105 is present.

[0021] The necking 105 is recognized both visually and by touch based on the surface shape of the test specimen 101. The inventors therefore considered the possibility of evaluating the presence or absence of necking 105 based on changes in the surface shape of the test specimen 101 and determining the forming limit. If necking 105 could be evaluated based on changes in the surface shape of the test specimen 101, it would be possible to directly measure the strain inside the necking 105 without approximating it. This finding solved the problems encountered in conventional methods, such as the strain distribution varying depending on the material properties (n value) of the metal plate, and the inability to appropriately approximate the strain distribution occurring on the surface of the test specimen 101 due to secondary and tertiary peaks observed in the strain distribution of high-strength steel plates, making it difficult to accurately determine the strain at the forming limit. The present invention was completed based on these findings and specifically comprises the following configurations.

[0022] The forming limit determination method for a metal plate according to the present invention determines the forming limit of a metal plate, and includes a forming test step, a forming limit analysis step, and a forming limit determination step. The forming test step includes a test piece preparation step of preparing a test piece having a predetermined grid or a pattern for strain analysis on a surface of the metal plate, and a step of taking sequential photographs of the surface of the test piece having the grid or the pattern for strain analysis on the surface. a strain and three-dimensional coordinate measuring step of analyzing images sequentially taken in the test piece forming step to measure strain occurring on the surface of the test piece and three-dimensional coordinates of the surface; and 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 perpendicular to a fracture occurring in the test piece, an evaluation point sequence setting step of setting an evaluation point sequence on the test piece to obtain a distribution of strain or three-dimensional coordinates at the fracture and its vicinity in the fracture orthogonal direction, and 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 includes a gradient perpendicular to the fracture direction 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 three-dimensional coordinate gradient in the direction perpendicular to the fracture.

[0023] In the fracture orthogonal direction gradient calculation step, a fracture orthogonal direction gradient of the plate thickness direction strain in the evaluation point sequence may be calculated.

[0024] In the fracture orthogonal direction gradient calculation process, 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] In the forming limit determination process, it is preferable to determine 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 to use 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.

[0026] In the forming test step, a plurality of test pieces having different shapes are prepared and formed, and in the forming limit analysis step, strain and three-dimensional coordinates in the evaluation point sequence are extracted for each of the plurality of test pieces, and in the forming limit determination step, the forming limit is determined for each of the plurality of test pieces to obtain a forming limit line.

[0027] A forming limit judgment system for metal plate according to the present invention is for judging the forming limit of a metal plate, and comprises a forming test apparatus, a forming limit analysis apparatus, and a forming limit judgment apparatus, wherein the forming test apparatus comprises 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 apparatus for sequentially photographing the surface of the test piece during the forming process of the test piece by the forming die, a strain and three-dimensional coordinate measuring apparatus for analyzing images of the surface of the test piece sequentially photographed by the imaging apparatus, and measuring strain occurring on the surface of the test piece and three-dimensional coordinates of the surface, and a database construction apparatus for storing the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture, and constructing a database, and the forming limit analysis apparatus comprises a forming test apparatus, a forming limit analysis apparatus, and a forming limit judgment apparatus. and a forming limit determination unit that determines the forming limit of the test piece based on the calculated gradient of strain or three-dimensional coordinates in the fracture orthogonal direction.

[0028] The forming limit determination device may calculate a gradient of the thickness direction strain in the direction perpendicular to fracture in the evaluation point sequence, and determine the forming limit of the test piece.

[0029] The forming limit determination device may convert three-dimensional coordinates in the evaluation point sequence into normal coordinates and tangential coordinates of the test piece, and calculate the gradient of the normal coordinates in the fracture orthogonal direction as the fracture orthogonal direction gradient of the three-dimensional coordinates.

[0030] 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 value, 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] The forming test device forms a plurality of test pieces having different shapes, the forming limit analysis device extracts the strain and three-dimensional coordinates in the evaluation point sequence for each of the plurality of test pieces, and the forming limit determination device determines the forming limit for each of the plurality of test pieces to obtain a forming limit line.

[0032] The forming limit judgment program for a metal sheet according to the present invention judges the forming limit of a metal sheet, and causes a computer to function as a forming limit analyzer and a forming limit judgment device of the forming limit judgment system for a metal sheet according to the present invention.

[0033] According to the present invention, by calculating the strain or the gradient of the three-dimensional coordinates on the surface of a metal plate test piece in the direction perpendicular to the fracture, it is possible to determine the occurrence of necking based on the change 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, it is possible to determine the forming limit of the 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.

[0034] FIG. 1 is a flow chart showing the process flow of a forming limit determination method for metal sheets according to an embodiment of the present invention. FIG. 2 is a diagram showing the shape of a metal sheet test piece used in an extension test in an embodiment and an example of the present invention. FIG. 3 is a diagram showing an example of a forming die used to form a test piece in the forming limit determination method for metal sheets and the forming limit determination device according to an embodiment of the present invention. FIG. 4 is a diagram showing the fracture orthogonal direction perpendicular to a fracture occurring in a formed test piece in the forming limit determination method for metal sheets according to an embodiment of the present invention. FIG. 5 is a graph explaining the fracture orthogonal direction gradient of strain related to determining the forming limit of a test piece in the forming limit determination method according to an embodiment of the present invention. FIG. 6 is a diagram showing the configuration of a forming limit determination system for metal sheets according to this embodiment. FIG. 7-1 is a graph showing the distribution of maximum principal strain on the surface of a formed test piece in an example ((a) forming step: 300 steps, (b) forming step: 500 steps, (c) forming step: 800 steps). Figure 7-2 is a graph showing the distribution of maximum principal strain on the surface of a formed test piece in an example ((d) forming step: 1000 steps, (e) forming step: 1100 steps, (f) forming step: 1160 steps). Figure 7-3 is a graph showing the distribution of maximum principal strain on the surface of a formed test piece in an example ((g) forming step: 1180 steps, (h) forming step: 1200 steps, (i) forming step: 1210 steps). Figure 8-1 is a graph showing the distribution of thickness direction strain and its gradient in the direction perpendicular to fracture on the surface of a formed test piece in an example ((a) forming step: 300 steps, (b) forming step: 500 steps, (c) forming step: 800 steps). Figure 8-2 is a graph showing the distribution of strain in the thickness direction and its gradient in the direction perpendicular to the fracture direction 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 8-3 is a graph showing the distribution of strain in the thickness direction and its gradient in the direction perpendicular to the fracture direction 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).Fig. 9 is a graph showing the transition of the necking ratio over the course of a test piece in an example. Fig. 10 is a forming limit diagram obtained in an example. Fig. 11 is a diagram showing 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 obtained by these methods ((a) Nakajima method, (b) Marciniak method, (c) forming limit diagrams obtained by both the Nakajima method and the Marciniak method). Fig. 12 is a graph showing an example of the distribution of strain occurring on the surface of a metal sheet. Fig. 13 is a diagram explaining a method for checking necking occurring in a metal sheet during a forming test ((a) cross-sectional view of necking occurring in a metal sheet, (b) visual confirmation of necking, (c) confirmation by touch).

[0035] <Method for Determining Forming Limit of Metal Sheet> The method for determining a 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 measuring step S15, and a database construction step S17.

[0037] (Test Piece Preparing Step) The test piece preparing step S11 is a step of preparing a test piece having a predetermined grid or strain analysis pattern on the surface of a metal plate.

[0038] 2A and 2B are diagrams showing specific examples of the test piece 101. Fig. 2A shows a disk-shaped test piece 101, and Figs. 2B and 2C show test pieces 101 in which arc-shaped cutout portions 101a are formed at positions on the periphery of the disk that face each other in the diametric direction, and the widths W of the central portions 101b are different.

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

[0040] (Test Piece Forming Step) 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 lattice or strain analysis pattern has been applied in the test piece preparation step S11.

[0041] In the test piece molding step S13, a molding die 11 equipped with a punch 11a, an upper die 11b, and a blank holder 11c, as shown in Fig. 3, is used to perform bulge molding of the test piece 101. The bulge molding 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 Fig. 3, but may also use a flat-headed punch 213 with a flat tip 213a as shown in Fig. 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, thereby obtaining images of the surface of the test piece 101 during each molding step. 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 three-dimensional coordinate measurement process) The strain and three-dimensional coordinate measurement process S15 is a process of analyzing the images sequentially taken in the test piece molding process 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). In DIC, the strain in two in-plane directions occurring on the surface of the test piece 101 and the three-dimensional coordinates of the surface (surface shape of the test piece 101) can be measured from the deformation state of a grid or strain analysis pattern attached to the surface of the test piece 101. In addition, in DIC, it is preferable to measure 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 Step) 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 a 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 measurement step S15, and the database construction step S17 are repeated. This repetition is performed until it is determined that a fracture has occurred in the test piece 101 (S19). In this way, a database can be constructed in which the strain occurring on the surface of the test piece 101 and the three-dimensional coordinates of the surface are stored in each molding step from the start of molding to fracture.

[0047] <Forming Limit Analysis Step> As shown in FIG. 1, the forming limit analysis step 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 Identifying Step) The fracture orthogonal direction identifying step S21 is a step of identifying 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 fractured portion 103 that occurred in the test piece 101, and (b) a necking 105 that leads to the fractured portion 103 in the test piece 101. The necking 105 is a location where the plate thickness is locally reduced in the A-A cross section perpendicular to the fractured portion 103. The direction parallel to the fractured portion 103 is the fracture direction, and the direction perpendicular to the fractured portion 103 is the fracture orthogonal direction.

[0050] (Evaluation point sequence setting step) The evaluation point sequence setting step S23 is a step of setting an evaluation point sequence on the test piece 101 for acquiring the distribution in the fracture orthogonal direction of the strain or three-dimensional coordinates at and near the fractured portion 103 that occurs in the test piece 101. The evaluation point sequence may be set at a predetermined interval along the fracture orthogonal direction so as to straddle the fractured portion 103 in the test piece 101, for example.

[0051] (Strain or three-dimensional 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 predetermined 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 Step> 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 Orthogonal Direction Gradient Calculation Step) 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 strain ε is calculated as shown in Fig. 5. The thickness strain ε can be calculated from the strains in two in-plane directions measured by DIC and extracted from a database using the law of constant volume.

[0057] Figure 5(a) shows the distribution of the fracture orthogonal direction gradient of the thickness direction strain calculated in the fracture orthogonal direction gradient calculation step S31, and Figure 5(b) shows the distribution of the fracture orthogonal direction of the thickness direction strain. In Figures 5(a) and (b), x is the coordinate in the fracture orthogonal direction of the evaluation point sequence, εz is the thickness direction strain, a is the fracture orthogonal direction gradient of the thickness direction strain, and n is the nth evaluation point set along the fracture orthogonal direction. The fracture orthogonal 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 Step) 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 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 for each forming step. When necking occurs in the test specimen 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 there is necking.

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

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

[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 the test piece 101 is formed using a flat-head punch 213 as in the Marciniak method shown in FIG. 11(b), the three-dimensional coordinates of the surface of the test piece 101 can be measured by measuring the coordinates in two in-plane directions on the surface of the test piece 101 and the coordinates in the out-of-plane direction perpendicular to these directions. In this case, of the measured three-dimensional coordinates, the coordinates in the out-of-plane direction can be acquired as the thickness direction coordinates.

[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 directly obtained. In this case, in the forming limit determination step S30, the three-dimensional coordinates in the evaluation point sequence are transformed into normal direction coordinates and tangential direction coordinates on the surface of the test piece 101, and the normal direction coordinates are set as thickness direction coordinates, with the tangential direction being set to coincide with the fracture orthogonal direction. As a result, the tangential direction gradient of the transformed normal direction coordinates can be calculated as the fracture orthogonal direction gradient of the thickness direction 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 it is determined that necking has occurred is calculated as the forming limit strain. This allows a forming limit diagram of the metal sheet to be obtained. For example, the forming limit strain may be the strain at the fractured portion in the forming step immediately prior to the forming step in which it is determined that necking has occurred.

[0068] <Forming Limit Judgment System for Metal Sheet> A forming limit judgment system 1 for a metal sheet (hereinafter referred to as "forming limit judgment system 1") according to this embodiment judges the forming limit of a metal sheet, and includes a forming test device 10, a forming limit analysis device 20, and a forming limit judgment device 30, as shown in FIG. 6 .

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

[0070] (Forming Mold) The forming mold 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 mold 11 can be exemplified by one including a punch 11a, an upper die 11b, and a blank holder 11c.

[0071] (Photographing 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. The photographing device 13 may be, for example, one that is composed of two cameras and that performs stereo photography of the surface of the test piece 101.

[0072] (Strain and three-dimensional 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 Creation Device) The database creation device 17 is a device that creates a database by storing 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.

[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 extraction unit 25. The forming limit analysis device 20 can be exemplified by a device 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 Identifying Unit) The fracture orthogonal direction identifying unit 21 identifies a fracture orthogonal direction that is orthogonal to the fracture 103 that occurs in the test piece 101 molded by the molding test device 10.

[0076] (Evaluation Point Sequence Setting Unit) The evaluation point sequence setting unit 23 sets an evaluation point sequence on the test piece 101 for acquiring the strain and three-dimensional coordinate distribution in the vicinity of the fractured portion 103 .

[0077] (Strain or Three-Dimensional Coordinate Extraction Unit) The strain or three-dimensional coordinate extraction unit 25 extracts the strain or three-dimensional coordinates of the evaluation point sequence in a predetermined forming step of the test piece 101 from the database.

[0078] <Forming Limit Judgment Device> The forming limit judgment device 30 has a fracture orthogonal direction gradient calculation unit 31 and a forming limit judgment unit 33. The forming limit judgment device 30 can be, for example, configured by a computer (such as a PC). In this case, each unit of the forming limit judgment device 30 functions when the CPU of the computer executes a predetermined program.

[0079] (Fracture Orthogonal Direction Gradient Calculation Unit) 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 .

[0080] (Forming Limit Determining Section) The forming limit determining section 33 determines the forming limit of the test piece 101 based on the strain in the calculated evaluation point sequence or the fracture orthogonal direction gradient of the three-dimensional coordinates.

[0081] The forming limit determination device 30 may calculate the fracture orthogonal direction gradient of the plate thickness direction strain in the evaluation point sequence using 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.

[0082] 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.

[0083] 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.

[0084] Furthermore, the forming limit determination device 30 determines, by the forming limit determination unit 33, that necking has occurred in a forming step in which the strain in the evaluation point sequence or the fracture orthogonal direction gradient of the three-dimensional coordinates exceeds a predetermined threshold value.

[0085] The forming limit determination system 1 according to this embodiment can obtain the forming limit line of a metal sheet. To do so, the forming test apparatus 10 forms a plurality of test pieces having different shapes, and the forming limit analysis apparatus 20 extracts 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. As a result, the forming limit determination system 1 can also obtain the forming limit line using the forming limit strains determined for the plurality of test pieces 101. The forming limit strain may be, for example, the strain at the fractured portion in the forming step immediately before the formation step in which necking is determined to have occurred.

[0086] <Forming Limit Judgment Program for Metal Sheet> An embodiment of the present invention can be configured as a forming limit judgment program for metal sheet that causes the forming limit analysis device 20 and the forming limit judgment device 30 implemented by a computer to function.

[0087] That is, the forming limit judgment program for a metal sheet according to this embodiment judges the forming limit of a metal sheet, and causes a computer to function as a forming limit analysis device 20 and a forming limit judgment device 30 shown in FIG. 6 .

[0088] The forming limit judgment 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.

[0089] 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 .

[0090] 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 gradient of the strain or the three-dimensional coordinates in the direction perpendicular to the fracture on the surface of the test piece is calculated. This makes it possible to determine the presence or absence of necking based on changes in the surface shape of the test piece, thereby enabling the forming limit of the metal sheet to be determined with high accuracy. Furthermore, 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 make it possible to determine the forming limit of the metal sheet while eliminating the influence of strain distribution due to material properties such as the material strength and work hardening rate of the metal sheet.

[0091] An experiment was conducted to verify the effects of the present invention, and the results will be described below.

[0092] The experiment was carried out by implementing the method for determining the forming limit of a metal sheet according to the present embodiment, and the forming of the metal sheet, analysis of the forming limit, and determination were carried out. A high-strength steel sheet with a tensile strength of 590 MPa and a thickness of 1.6 mm was used as the metal sheet. As shown in Figures 2(b) and 2(c) above, a test piece 101 was prepared, with circular-arc cutouts 101a formed at diametrically opposed positions on the peripheral edge of the disc having a diameter of 100 mm, and the width W of the central portion 101b was set to 32 mm or 48 mm.

[0093] The test specimen 101 was formed using a hydraulic deep drawing testing machine equipped with a forming die 11 consisting of a 25 mm radius spherical punch 11a, an upper die 11b, and a blank holder 11c. To prevent the test specimen 101 from flowing into the die during forming, a blank holder force of 980 kN was applied to the blank holder 11c, and the punch speed was set to 5 mm / min. Two image analysis cameras installed above the forming die 11 sequentially photographed the surface of the test specimen 101 at intervals of once per second from the start of forming until fracture occurred.

[0094] 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.

[0095] 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.

[0096] Next, as shown in Figure 7-3, the fracture orthogonal direction perpendicular to the fractured part of the test piece 101 was identified, and an evaluation point sequence was set on the test piece 101 to obtain the distribution of strain and three-dimensional coordinates near the fractured part. Then, the strain in the evaluation point sequence was extracted from the database of strain and three-dimensional coordinates constructed by the forming test.

[0097] Next, the thickness direction strain was calculated from the strains at the extracted evaluation points, 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.

[0098] 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 specimen 101. Then, for each forming step in which the test specimen 101 was formed, the ratio of the gradient of the thickness direction strain in the direction perpendicular to the fracture to the threshold value (strain gradient ratio) 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.

[0099] Figures 8-1 to 8-3 show the results of the thickness direction strain and its gradient in the direction perpendicular to the fracture direction for 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 the zero on the horizontal axis represents the center position of the fracture that occurred in test piece 101.

[0100] As shown in Figures 8-1 to 8-3, as the forming steps progress, the thickness 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 strain. It can be seen that in the forming step 1160 (see Figure 8-2(f)), the strain gradient ratio reaches a maximum value of 1.

[0101] Figure 9 shows the transition of the necking ratio from the start of forming to fracture of the test piece 101. As shown in Figure 9, the necking ratio increases as the forming steps progress, and it can be seen that the necking ratio exceeds 1 in forming step 1160. As such, from the results shown in Figures 8-1 to 8-3 and 9, it was determined that the forming limit was reached in forming step 1160.

[0102] Furthermore, in the examples, forming tests were performed using a plurality of test pieces 101 in which the shape of the notch 101a was changed, and the forming limit was determined to obtain the forming limit strain. Table 1 shows the forming limit strain obtained using a plurality of test pieces 101 with different shapes. Furthermore, Figure 10 shows the forming limit line obtained using a plurality of test pieces 101 with different shapes.

[0103] 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.

[0104] According to the present invention, it is possible 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.

[0105] DESCRIPTION OF SYMBOLS 1 Forming limit judgment system 10 Forming test device 11 Forming mold 11a Punch 11b Upper die 11c Blank holder 13 Photography device 15 Strain and three-dimensional coordinate measuring device 17 Database construction device 20 Forming limit analysis device 21 Fracture orthogonal direction identification unit 23 Evaluation point sequence setting unit 25 Strain or three-dimensional coordinate extraction unit 30 Forming limit judgment device 31 Fracture orthogonal direction gradient calculation unit 33 Forming limit judgment unit 101 Test piece 101a Notch portion 101b Center portion 103 Fracture portion 105 Neck 107 File portion 111 Light 201 Forming mold 203 Ball head punch 203a Tip portion 205 Upper die 207 Blank holder 211 Forming mold 213 Flat head punch 213a Tip 215 Driving seat

Claims

1. A method for determining the forming limit of a metal plate for determining the forming limit of a metal plate, comprising: a forming test stage; a forming limit analysis stage; and a forming limit determination stage, wherein the forming test stage comprises: a test piece preparation step of preparing a test piece having a predetermined lattice or strain analysis pattern on the surface of the metal plate; a test piece formation step of forming the test piece while sequentially photographing the surface of the test piece having the lattice or strain analysis pattern; a strain and three-dimensional coordinate measurement step of analyzing the images sequentially photographed in the test piece formation step to measure strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; and a database construction step of storing the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture and constructing a database, wherein the forming limit analysis stage comprises: a fracture orthogonal direction identification step of identifying a fracture orthogonal direction perpendicular to a fracture occurring in the test piece; a strain or three-dimensional coordinate extraction step of extracting from the database the strain or three-dimensional coordinates in the evaluation point sequence at a predetermined forming step of the test piece, wherein the forming limit determination stage comprises: a fracture orthogonal direction gradient calculation 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; and a forming limit determination step of determining the forming limit of the test piece based on the calculated fracture orthogonal direction gradient of the strain or three-dimensional coordinates.

2. A forming limit determination method for metal sheets according to claim 1, wherein in the fracture orthogonal direction gradient calculation step, the fracture orthogonal direction gradient of the sheet thickness direction strain in the evaluation point sequence is calculated.

3. A method for determining the forming limit of a metal plate according to claim 1, wherein in the fracture orthogonal direction gradient calculation step, the 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. A method for determining the forming limit of a metal sheet according to any one of claims 1 to 3, wherein 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 prior to the step in which it is determined that necking has occurred is taken as the forming limit strain.

5. A method for determining the forming limit of a metal sheet according to claim 4, wherein, in the forming test stage, a plurality of test pieces having different shapes are prepared and formed; in the forming limit analysis stage, strain and three-dimensional coordinates in the evaluation point sequence are extracted for each of the plurality of test pieces; and in the forming limit determination stage, 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 judgment system for judging the forming limit of a metal plate, comprising: a forming test device; a forming limit analysis device; and a forming limit judgment device, wherein the forming test device comprises: a forming die for forming a test piece of the metal plate having a predetermined grid or strain analysis pattern on its surface; a photographing device for sequentially photographing the surface of the test piece during the forming process of the test piece using the forming die; a strain and three-dimensional coordinate measuring device for analyzing the images of the test piece surface sequentially photographed by the photographing device and measuring the strain occurring on the surface of the test piece and the three-dimensional coordinates of the surface; and a database construction device for storing the measured strain and three-dimensional coordinates in chronological order from the start of forming to fracture and constructing a database, wherein the forming limit analysis device comprises: a fracture orthogonal direction specifying unit for specifying a fracture orthogonal direction perpendicular to a fracture occurring in the test piece formed by the forming test device; a strain or three-dimensional coordinate extraction unit that extracts, from the database, strain or three-dimensional coordinates in the evaluation point sequence at a predetermined forming step of the test piece; and a fracture orthogonal direction gradient calculation unit that calculates a fracture orthogonal direction gradient of 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 fracture orthogonal direction gradient of strain or three-dimensional coordinates.

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

8. A forming limit determination system for metal sheets according to claim 6, wherein the forming limit determination device 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.

9. A forming limit determination system for metal sheets as described in any one of claims 6 to 8, 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 value, 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.

10. A forming limit judgment system for metal sheets according to claim 9, wherein the forming test device forms 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, and the forming limit judgment device judges the forming limit for each of the plurality of test pieces and obtains a forming limit line.

11. A forming limit determination program for metal sheets for determining the forming limits of metal sheets, characterized in that it has a function of causing a computer to execute the forming limit determination program as a forming limit analysis device and a forming limit determination device of the metal sheet forming limit determination system according to any one of claims 6 to 10.

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