Sheet metal forming limit acquisition method, sheet metal forming limit surface creation method, sheet metal forming limit surface creation system, and sheet metal forming limit surface creation program

Abstract

To provide a method for acquiring a forming limit of a metal plate, a method for creating a forming limit surface of the metal plate, a system for creating the forming limit surface of the metal plate, and a program for creating the forming limit surface of the metal plate for determining the forming limit of the metal plate in consideration of an influence of a force in a plate thickness direction and a strain path.SOLUTION: The forming limit acquisition method for a metal sheet according to the present invention performs a forming test of a metal sheet with a plurality of forming dies 11 having different shapes so as to generate various forces in the sheet thickness direction and with various strain paths, and obtains a force in the sheet thickness direction generated in a test piece 100 of the formed metal sheet, a strain path index representing the strain path of the formed test piece, and an equivalent plastic strain generated in the formed test piece as indices of the forming limit of the metal sheet.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a metal plate forming limit acquisition method for determining the forming limit of a metal plate, a metal plate forming limit surface creation method for creating a metal plate forming limit surface, a metal plate forming limit surface creation system, and a metal plate forming limit surface creation program. [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 a metal sheet test piece is varied at several levels, and the strain ratio in the major and minor axes of the test piece is changed, thereby measuring the strain in both the major and minor axes at the time of fracture of the test piece.

[0005] Generally, in forming tests of metal sheets, the test piece undergoes uniform deformation, followed by a process in which strain is concentrated at a specific location on the test piece. 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 breaks. In press forming, the occurrence of necking can result in a defective product even if it does not result in fracture (crack). 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, as shown by plot 1 in Fig. 10, the strain distribution in the direction intersecting the fractured portion (X direction) of a test piece formed until fracture is measured, and the measured strain distribution is approximated to a curve expressed by the following equation, as shown by solid line 2 in Fig. 10. Then, from the strain distribution Ex approximated by the equation below, the maximum value of strain indicated by arrow 6 in Fig. 10 is calculated, and this maximum value is taken as the forming limit strain.

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[0007] [Non-Patent Document 1] ISO 12004-2:2008, Metallic materials - Sheet and strip - Determination of forming-limit curves, 2008. Summary of the Invention [Problem to be solved by the invention]

[0008] Non-Patent Document 1 describes the Nakajima method and the Marciniak method as methods for determining the forming limit by a stretch test of a test piece 100, as shown in FIG. As shown in Figure 11(a), the Nakajima method involves bulging a test piece 100 using a molding die 201 equipped with a spherical punch 203 having a spherical-shaped 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 molding die 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 dummy sheet 215 between the flat-head punch 213 and the test piece 100 to bulge-mold the test piece 100.

[0009] Comparing the Nakajima method and the Marciniak method, the Nakajima method is a forming test in which the test piece 100 conforms to the shape of the tip 203a of the ball-head punch 203, so a large force in the thickness direction is applied to the fracture part of the test piece 100 that comes into contact with the tip 203a. In contrast, the Marciniak method is a forming test in which a dummy sheet 215 is sandwiched between the test piece 100 to prevent direct contact with the tip 213a of the flat-head punch 213, so no force in the thickness direction is applied to the fracture part.

[0010] In the Nakajima method, the test piece 100 is subjected to equibiaxial deformation in the early stage of forming until it fits into the tip 203a of the spherical-head punch 203, and then formed along a predetermined strain path, so strictly speaking, the forming limit is measured when the strain path changes. On the other hand, in the Marciniak method, the test piece 100 is formed using a flat-head punch 213 whose tip 213a is flat, so the forming limit is measured when the strain path is constant from the early stage of forming to fracture.

[0011] Generally, as shown in Figure 11(c), the forming limit line obtained by the Nakajima method has a strain amount just before necking occurs that is about 1 to 2% larger. In press forming of high-strength steel sheets with low ductility, even a slight difference in the amount of strain can make a difference in the occurrence of necking. For this reason, 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 amount measured in actual press-formed products or the strain amount obtained by press forming analysis using CAE.

[0012] However, even under press forming conditions predicted by the Nakajima method as no cracking would occur based on the strain obtained from press forming analysis, cracks sometimes occurred in actual press-formed products, especially press-formed products made of high-strength steel sheets of 980 MPa or higher. Also, even under press forming conditions predicted as likely to cause cracking using the Marciniak method, cracks sometimes did not occur in the actual press-formed products. Thus, when the presence or absence of cracking was predicted by press forming analysis based on the forming limit line created by the conventional method, there were many cases where the predicted presence or absence of cracking in the actual press-formed products was significantly different, which was problematic.

[0013] In particular, it is believed that in actual press-formed products, the force in the thickness direction generated during the press-forming process varies depending on the part, and the strain path is also different. However, the conventional method described above was unable to determine the forming limit by taking into account the force in the thickness direction and the strain path.

[0014] The present invention has been made to solve the above-mentioned problems, and aims to provide a method for obtaining the forming limit of a metal plate, which can determine the forming limit of a metal plate by taking into account the influence of the force in the plate thickness direction and the strain path, a method for creating a forming limit surface of a metal plate, a system for creating a forming limit surface of a metal plate, and a program for creating a forming limit surface of a metal plate. [Means for solving the problem]

[0015] (1) The method for obtaining the forming limit of a metal plate according to the present invention is characterized in that a forming test of the metal plate is performed using a plurality of tools having different shapes that generate various forces in the plate thickness direction and various strain paths, and the force in the plate thickness direction generated in a test piece of the formed metal plate, a strain path index representing the strain path of the formed test piece, and the equivalent plastic strain generated in the formed test piece are obtained as indicators of the forming limit of the metal plate.

[0016] (2) The method for creating a forming limit surface of a metal plate according to the present invention involves conducting a forming test of a metal plate using a plurality of tools having different shapes that generate various forces in the plate thickness direction and various strain paths, and creating a forming limit surface of the metal plate that is expressed by the relationship between the force in the plate thickness direction that occurs in a test piece of the formed metal plate, a strain path index that represents the strain path of the formed test piece, and an equivalent plastic strain that occurs in the formed test piece, The method includes a forming test step, a forming limit analysis step, and a forming limit surface creation step, The molding test step includes: a test piece preparation step of preparing a plurality of test pieces having different shapes and having a predetermined lattice or strain analysis pattern applied to the surface; a test piece forming step of forming each test piece using a plurality of tools having different shapes and various strain paths while photographing the surface of the test piece; a strain measurement step of analyzing the photographed images of the surfaces of the test pieces and measuring strains occurring in the test pieces; a thickness direction force acquisition step of determining a thickness direction force at a fracture portion occurring in each of the molded test pieces; a strain database construction step of storing the strains measured in the strain measurement step for each of the formed test pieces in chronological order from the start of forming to the occurrence of fracture, and constructing a strain database; The forming limit analysis step includes: an evaluation point sequence setting step of setting an evaluation point sequence in each of the molded test pieces to acquire a strain distribution in the vicinity of the fracture portion generated in each of the molded test pieces; a strain distribution acquisition step of extracting the strain of the evaluation point sequence set for each of the test pieces from the strain database and acquiring a strain distribution in the vicinity of the fractured portion; a forming limit acquisition step of determining a forming limit of each of the test pieces based on the acquired strain distribution, and calculating a strain path index and an equivalent plastic strain at the determined forming limit, The forming limit surface creation step includes: a forming limit plotting step of plotting the force in the plate thickness direction at the fracture portion, the strain path index at the forming limit, and the equivalent plastic strain, which are obtained for each of the formed test pieces, in a three-dimensional coordinate space; and a forming limit surface creation process for creating a forming limit surface of the metal plate based on a group of plot points of the force in the plate thickness direction at the fracture portion plotted in the three-dimensional coordinate space, and the strain path index and equivalent plastic strain at the forming limit.

[0017] (3) In the above (2), The step of obtaining the force in the plate thickness direction is characterized in that the force in the plate thickness direction is obtained by obtaining the surface pressure generated at the fracture portion of each of the molded test pieces.

[0018] (4) In the above (3), The surface pressure is measured by placing pressure-sensitive paper between the tool and each of the test pieces during the test piece molding process, or is calculated by finite element method analysis that reproduces the molding of each of the test pieces during the test piece molding process.

[0019] (5) In the above (2), The thickness direction force acquisition process is characterized in that the thickness direction stress occurring at the fracture portion of each of the test pieces formed in the test piece forming process is obtained as the thickness direction force.

[0020] (6) In the above (5), The stress in the thickness direction is calculated by a finite element method analysis that reproduces the forming of each of the test pieces in the test piece forming step.

[0021] (7) In any one of (2) to (6) above, The forming limit obtaining step is characterized in that a strain increment ratio expressed by the following formula is calculated as the strain path index.

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[0022] (8) In any one of (2) to (6) above, The forming limit obtaining step is characterized in that the stress triaxiality expressed by the following formula is calculated as the strain path index.

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[0023] (9) In any one of (2) to (8) above, In the forming limit surface creation step, a polygonal surface is created that is made up of a plurality of triangular planes that connect two adjacent plot points among the plot point groups for a plurality of the test pieces formed using the tool having the same shape, and one plot point that is closest to the line segment connecting the two plot points among the plot point groups for a plurality of the test pieces formed using the tool having a shape different from that of the two plot points.

[0024] (10) In any one of (2) to (8) above, In the forming limit surface creation step, a forming limit plane or a forming limit curved surface is assumed, the sum of squares of the perpendicular distances between the assumed forming limit plane or the forming limit curved surface and each plot point of the group of plot points in the three-dimensional coordinate space is calculated, and the forming limit plane or the forming limit curved surface is determined so that the calculated sum of squares is minimum.

[0025] (11) In any one of (2) to (8) above, In the forming limit surface creation step, a forming limit plane or a forming limit curved surface is assumed, a sum of squares weighted on the perpendicular distance between the assumed forming limit plane or the formed limit curved surface and each plot point of the group of plot points in the three-dimensional coordinate space is calculated, and the forming limit plane or the formed limit curved surface is determined so that the calculated sum of squares is minimized.

[0026] (12) In the above (10), In the forming limit surface creation step, the forming limit surface is created by combining a plurality of forming limit planes and / or forming limit curved surfaces.

[0027] (13) In the above (11), In the forming limit surface creation step, the forming limit surface is created by combining a plurality of forming limit planes and / or forming limit curved surfaces.

[0028] (14) The forming limit surface creation system for a metal plate according to the present invention performs a forming test of a metal plate using a plurality of tools having different shapes that generate various forces in the plate thickness direction and various strain paths, and creates a forming limit surface of the metal plate that is expressed by the relationship between the force in the plate thickness direction generated in a test piece of the formed metal plate, a strain path index that represents the strain path of the formed test piece, and an equivalent plastic strain generated in the formed test piece, The apparatus includes a forming test section, a forming limit analysis section, and a forming limit surface creation section, The molding test section a plurality of tools having different shapes for forming a plurality of test pieces having different shapes, each of which has a predetermined lattice or strain analysis pattern applied to its surface, so that various forces in the thickness direction are generated in each of the test pieces; an imaging device that images the surface during the process of forming each of the test pieces using multiple tools and various strain paths; a strain measuring device that analyzes the captured image of the surface of each of the test pieces and measures strain occurring in each of the test pieces; a thickness direction force acquisition device for determining a thickness direction force at a fracture portion generated in each of the molded test pieces; a strain database construction device that stores the strain measured by the strain measuring device for each of the formed test pieces in chronological order from the start of forming to the occurrence of fracture, and constructs a strain database; The forming limit analysis unit an evaluation point sequence setting device that sets an evaluation point sequence on the test piece to acquire strain distribution in the vicinity of the fracture portion generated in each of the molded test pieces; a strain distribution acquisition device that extracts the strain of the evaluation point sequence set on each of the test pieces from the strain database and acquires the strain distribution in the vicinity of each of the fractured portions; a forming limit acquisition device that determines a forming limit of each of the test pieces based on the acquired strain distribution, and calculates a strain path index and an equivalent plastic strain at the determined forming limit, The forming limit surface creation unit a forming limit plotting device that plots the force in the plate thickness direction at the fracture portion, the strain path index at the forming limit, and the equivalent plastic strain, which are obtained for each of the formed test pieces, in a three-dimensional coordinate space; and a forming limit surface creation device that creates a forming limit surface of the metal plate based on a group of plot points of the force in the plate thickness direction at the fracture part, and the strain path index and equivalent plastic strain at the forming limit, which are plotted in the three-dimensional coordinate space.

[0029] (15) The forming limit surface creation program for a metal plate according to the present invention creates a forming limit surface for the metal plate, which is expressed by the relationship between a force in the thickness direction generated in a test piece of the metal plate formed in a forming test of the metal plate using a plurality of tools having different shapes so as to generate various forces in the thickness direction and various strain paths, a strain path index, and an equivalent plastic strain, The present invention is characterized by having a function of causing a computer to function as the forming limit analysis unit and the forming limit surface creation unit of the metal plate forming limit surface creation system described in (14) above. [Effects of the Invention]

[0030] In the present invention, forming tests of metal sheets are performed using a plurality of tools with different shapes and various strain paths, and the force in the thickness direction generated in the test piece, the strain path index of the test piece in the forming test, and the equivalent plastic strain generated in the test piece are obtained as indexes of the forming limit of the metal sheet. This makes it possible to determine the forming limit of the metal sheet by taking into account the influence of the force in the thickness direction and the strain path. Furthermore, according to the present invention, by plotting the force in the plate thickness direction, the strain path index, and the equivalent plastic strain obtained as indexes of the forming limit in a three-dimensional coordinate space, it is possible to create a forming limit surface of a metal plate expressed by the relationship between the force in the plate thickness direction, the strain path index, and the equivalent plastic strain. [Brief explanation of the drawings]

[0031] [Figure 1] FIG. 2 is a flowchart showing a process flow of a method for creating a forming limit surface of a metal plate according to an embodiment of the present invention. [Figure 2] FIG. 1 is a diagram illustrating the relationship between the strain increment ratio and the equivalent plastic strain at the forming limit of test pieces formed by different deformation paths. [Figure 3] FIG. 1 is a diagram showing a forming die, which is an example of a tool used to form a metal plate test piece in a method for obtaining the forming limit of a metal plate, a method for creating a forming limit surface of a metal plate, and a system for creating a forming limit surface of a metal plate according to an embodiment of the present invention. [Figure 4] 1A and 1B are diagrams showing the specific shape of the tip of a punch used to form a test piece from a metal plate in the embodiments and examples of the present invention. [Figure 5] 1A and 1B are diagrams showing specific examples of the shape of a test piece used in a forming test for creating a forming limit surface of a metal plate in the present embodiment and examples. [Figure 6]1 is a diagram illustrating a configuration of a forming limit surface creation system for a metal plate according to an embodiment of the present invention; [Figure 7] FIG. 10 is a diagram showing a process flow for creating a forming limit surface of a metal plate in an embodiment. [Figure 8] 1 is a graph showing a method for calculating the strain increment ratio at the forming limit of test pieces formed using forming dies and strain paths with different shapes in the examples. [Figure 9] FIG. 2 is a diagram showing a forming limit surface created in an example, which is expressed by the relationship between force in the plate thickness direction (surface pressure), strain path index (strain increment ratio), and equivalent plastic strain. [Figure 10] 1 is a graph illustrating a conventional method for determining the forming limit strain from the strain distribution measured by a forming test of a metal plate. [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). DETAILED DESCRIPTION OF THE INVENTION

[0032] Before describing the embodiments of the present invention, the background to the invention will be explained. Note that the dimensions and other specific numerical values ​​shown in the following description and drawings are merely examples to facilitate understanding of the present invention and are not intended to limit the present invention. Furthermore, in this specification and drawings, elements having substantially the same functions and configurations are designated by the same reference numerals, and redundant descriptions are omitted or simplified.

[0033] <Background to the invention> The inventors have investigated a method for determining the forming limit of a metal sheet, taking into consideration the influence of the force in the sheet thickness direction and the strain path.

[0034] First, with regard to the force in the thickness direction, based on a comparison of the Nakajima method and the Marciniak method mentioned above, we came up with the idea of ​​conducting forming tests with variously modified shapes of the tip of the forming die (punch), and determining the force in the thickness direction at the fracture point that occurs in the test piece as an index of the forming limit.

[0035] Regarding the strain path, we focused on the following findings obtained from forming tests using the Marciniak method. Normally, in forming tests using the Marciniak method, the strain path remains constant, but sometimes forming tests are performed by intentionally changing the strain path, for example by stopping forming midway, changing the notch shape of the test piece, and then resuming forming. When forming is performed by changing the strain path in this way, if the strain increment ratio (the ratio of the increment of the minimum principal strain to the increment of the maximum principal strain) at the time of final necking is the same as the strain increment ratio when forming is performed on a constant strain path, then the equivalent plastic strain at the forming limit for both will be the same.

[0036] Figure 2 is a graph showing the transition of the maximum principal strain and minimum principal strain in the test specimens formed using two different deformation paths, 1 and 2, from the start of forming to the end of forming when necking occurs. In Figure 2, for both deformation path 1 and deformation path 2, the squares indicate the start of forming, and the stars indicate the occurrence of necking. In deformation path 1, the strain increment ratio β1 is constant at 0.0 from the start of forming to the occurrence of necking, i.e., the strain path is constant. In contrast, for deformation path 2, the strain increment ratio in the early stage of forming is β 2,1 = 1.0, and the strain increment ratio until the end of forming is β 2,2 = 0.0, which is the case when the strain path changes during the forming process.

[0037] Deformation path 1 and deformation path 2 represent different strain paths for forming the test specimen, but the strain increment ratio at the time of necking is the same in both cases (β1 = β 2.2 =0.0), as mentioned above, the equivalent plastic strain at the forming limit is the same (ε eq1 =ε eq2 ).

[0038] In the deformation path 2, the strain increment ratio β 2,1 The equivalent plastic strain generated in the test piece formed along the strain path is defined as ε. eq,β2,1 , strain increment ratio β 2,2 The equivalent plastic strain generated in the test piece formed along the strain path is defined as ε. eq,β2,2 Then, the equivalent plastic strain ε at the time of necking (forming limit) is eq2 is the equivalent plastic strain (ε eq,β2,1 +ε eq,β2,2 ).

[0039] Therefore, even if the strain path changes as in deformation path 2, if the strain increment ratio is the same as that of deformation path 1, which has a constant strain path, the equivalent plastic strain accumulated from the start of forming to the forming limit in deformation path 2 is equal to the equivalent plastic strain at the forming limit (when necking occurs) of deformation path 1 (ε eq1 =ε eq,β2,1 +ε eq,β2,2 ).

[0040] From this, the inventors came to the idea that the strain increment ratio and equivalent plastic strain at the forming limit can be used as indicators representing the forming limit of a metal sheet.

[0041] Based on the above investigations, the inventors have found that it is possible to express the forming limit of a metal sheet by taking into account the influence of the force in the thickness direction and the strain path, by determining the force in the thickness direction at the fracture part of a formed test piece, and the strain increment ratio and equivalent plastic strain of the test piece at the forming limit as indices of the forming limit.

[0042] The present invention has been completed based on the above investigations, and its specific configuration is as follows.

[0043] <Method for obtaining forming limits for metal sheets> The method for obtaining the forming limit of a metal sheet according to this embodiment involves conducting forming tests of the metal sheet using a plurality of tools with different shapes that generate various forces in the thickness direction and various strain paths. The method for obtaining the forming limit of a metal sheet then obtains, as indicators of the forming limit of the metal sheet, the force in the thickness direction generated in a test piece of the formed metal sheet, a strain path index that represents the strain path of the formed test piece, and the equivalent plastic strain generated in the formed test piece.

[0044] FIG. 3 shows, as an example of a tool for forming the test piece 100, a forming die 11 equipped with a punch 11a, an upper die 11b, and a blank holder 11c.

[0045] As shown in FIG. 3, the punch 11a has a spherical surface with a radius of curvature R, that is, a spherical-head shaped tip portion 11a1 with a curvature ρ (=1 / R) greater than zero. Fig. 4 shows an example of a specific shape of the tip 11a1 of the punch 11a. The punch 11a is not limited to having a spherical tip 11a1 as shown in Figs. 4(a) to (c), but may have a flat tip 11a1 (with a radius of curvature R = ∞) as shown in Fig. 3(d). In other words, the punch 11a has a tip 11a1 with a curvature ρ (= 1 / R) of 0 or more.

[0046] As the metal plate test piece 100, test pieces 101 and 103 having the shapes shown in FIG. 5 can be exemplified in order to determine the forming limit under various strain paths (equiaxial deformation, non-uniform biaxial deformation, plane strain deformation, uniaxial deformation).

[0047] FIG. 5(a) shows a disk-shaped test piece 101, which is suitable for determining the forming limit of equibiaxial deformation. 5(b) and (c) show test piece 103 in which arc-shaped cutout portions 103a are formed at diametrically opposing positions on the disc-shaped peripheral edge, and the width W of the central portion 103b is different. As the width W of the central portion 103b of test piece 103 is narrowed, the deformation of test piece 103 changes from equibiaxial deformation to non-equilibrium biaxial deformation and plane strain deformation, gradually approaching uniaxial tension, and is therefore suitable for determining the forming limit for these strain paths.

[0048] The force in the thickness direction used as an index of the forming limit is the force in the thickness direction at the fractured portion of the test piece 100 formed until the fractured portion occurs. The force in the thickness direction generated in the test piece 100 can be varied by changing the shape of the tool (for example, the radius of curvature of the tip 11a1 of the punch 11a) to form the test piece 100.

[0049] In the method for obtaining the forming limit of a metal plate according to this embodiment, the force in the plate thickness direction is obtained as the surface pressure generated at the fractured portion of the formed test piece 100. The surface pressure can be obtained by the method described below.

[0050] The strain path index, which is an index of the forming limit, is the strain increment ratio at the forming limit of the formed test piece 100. The strain increment ratio of the test piece 100 can be changed in various ways depending on the shape of the tool (for example, the radius of curvature of the tip 11a1 of the punch 11a) and the shape of the test piece (for example, the width W of the central part 103b of the test piece 103).

[0051] The equivalent plastic strain used as an index of the forming limit is the equivalent plastic strain at the forming limit of the formed test piece 100. The equivalent plastic strain generated in the test piece 100 varies depending on the shape of the tool (the radius of curvature of the tip 11a1 of the punch 11a) and the shape of the test piece 100 (the width W of the central part 103b of the test piece 103).

[0052] The method for obtaining the forming limit of a metal sheet according to this embodiment does not particularly limit the method for obtaining the strain increment ratio and equivalent plastic strain that are used as indicators of the forming limit, as long as the strain increment ratio and equivalent plastic strain at the forming limit are obtained using the same standard for test pieces 100 formed using tools with different shapes (such as punches 11a with different curvatures at the tip portions 11a1).

[0053] For example, a test piece 100 with a marking (a grid or a pattern for strain analysis) on its surface is formed until it breaks, and the maximum principal strain and minimum principal strain at the forming limit (for example, when necking occurs in the test piece 100) are measured from the shape of the marking near the break. The strain increment ratio and equivalent plastic strain may then be calculated using the measured maximum principal strain and minimum principal strain, or may be calculated by the method described below.

[0054] As described above, in the method for obtaining the forming limit of a metal sheet according to this embodiment, forming tests of a metal sheet are performed using a plurality of forming dies 11 with different shapes and various strain paths, and the force in the thickness direction generated in the test piece 100, the strain path index of the test piece 100 in the forming test, and the equivalent plastic strain generated in the test piece 100 are obtained as indexes of the forming limit of the metal sheet. This makes it possible to obtain the forming limit of a metal sheet by taking into account the influence of the force in the thickness direction and the strain path.

[0055] In the above explanation, the surface pressure generated at the fractured portion of the molded test piece 100 is determined as the force in the thickness direction, but the present invention may also be directed to determining the stress in the thickness direction at the fractured portion of the molded test piece 100. The stress in the thickness direction can be determined by the method described below.

[0056] Furthermore, in the method for obtaining the forming limit of a metal sheet according to this embodiment, the strain increment ratio is determined as the strain path index representing the strain path of the formed test piece 100. However, the stress triaxiality may also be determined as the strain path index. The stress triaxiality can be determined by the method described below.

[0057] <Method for creating the forming limit surface of a metal sheet> As a specific example of the method for obtaining the forming limit of a metal plate according to this embodiment, a method for creating a forming limit surface of a metal plate will be described. In the following description, it is assumed that the forming die 11 shown in FIG. 3 is used as a tool for forming the test piece 100.

[0058] The method for creating a forming limit surface for a metal plate according to this embodiment involves conducting a forming test of the metal plate using a plurality of tools with different shapes and various strain paths so as to generate various forces in the plate thickness direction. The method for creating a forming limit surface for a metal plate creates a forming limit surface for the metal plate that is expressed by the relationship between the force in the plate thickness direction generated in a test piece of the formed metal plate, a strain path index that represents the strain path in the forming test, and the equivalent plastic strain generated in the formed test piece. As shown in FIG. 1, the method for creating a forming limit surface of a metal sheet according to this embodiment includes a forming test step S10, a forming limit analysis step S20, and a forming limit surface creation step S30.

[0059] <Molding test step> As shown in FIG. 1, the forming test step S10 includes a test piece preparation step S11, a test piece forming step S13, a strain measurement step S15, a thickness direction force acquisition step S17, and a strain database construction step S19.

[0060] (Test piece preparation process) The test piece preparation step S11 is a step of preparing a plurality of test pieces 100 of different shapes, each having a predetermined lattice or strain analysis pattern applied to the surface of a metal plate, as shown in FIG.

[0061] The strain analysis pattern applied to the surface of the test piece 100 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 100.

[0062] In the test piece preparation step S11, a plurality of test pieces 100 with different shapes are prepared. The shape of the test piece 100 may be appropriately determined so that the forming limit can be determined for various strain paths (equi-biaxial deformation, non-uniform biaxial deformation, plane strain deformation, and uniaxial deformation).

[0063] Specific examples of the shape of the test piece 100 include a circular test piece 101 and a test piece 103 having a notch 103a formed in the outer edge of the circular shape, as shown in Fig. 5. For the test piece 103 having the notch 103a, it is preferable to prepare test pieces in which the width W of the central portion 103b is changed at multiple levels.

[0064] (Test piece molding process) The test piece molding step S13 is a step of molding each test piece 100 while taking images of the surface using a plurality of molding dies 11 with different shapes and various strain paths.

[0065] In the test piece molding step S13, a test piece 100 is molded for each combination of one molding die 11 out of a plurality of molding dies 11 having different shapes and one test piece 100 out of a plurality of test pieces 100 having different shapes.

[0066] In the test piece molding step S13, the surface of the test piece 100 may be photographed by placing a camera (photographing device) above the molding die 11 and photographing the surface of the test piece 100 during the molding process at predetermined time intervals.

[0067] (Strain measurement process) The strain measuring step S15 is a step of analyzing the image of the surface of each test piece 100 taken in the test piece forming step S13, and measuring the strain occurring in each test piece 100.

[0068] In this embodiment, digital image correlation (DIC) is used to measure the strain on the surface of the test piece 100. In DIC, it is possible to measure the strain in two in-plane directions on the surface of the test piece 100 from the deformation state of a lattice or strain analysis pattern attached to the surface of the test piece 100. Furthermore, 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 100.

[0069] (Process for obtaining force in the plate thickness direction) The thickness direction force acquisition step S17 is a step of obtaining the force in the thickness direction at the fracture portion generated in each test piece 100 formed in the test piece forming step S13.

[0070] In this embodiment, the plate thickness direction force acquisition step S17 obtains, as the plate thickness direction force, the surface pressure generated at the fractured portion of each test piece 100 formed in the test piece forming step S13. The surface pressure generated at the fractured portion can be measured by placing pressure-sensitive paper 105 between the molding die 11 and each test piece 100 and molding it in the test piece molding step S13, as shown in Fig. 3. The surface pressure generated at the fractured portion can also be calculated by finite element method analysis that reproduces the molding of each test piece 100 in the test piece molding step S13.

[0071] In the thickness direction force acquisition step S17, the thickness direction stress occurring at the fractured portion of each formed test piece 100 may be obtained as the force in the thickness direction. In this case, in the thickness direction force acquisition step S17, the thickness direction stress can be calculated by a finite element method analysis that reproduces the formation of each test piece 100 in the test piece formation step S13. In such a finite element method analysis, it is preferable to divide the test piece into elements using solid elements.

[0072] (Strain database construction process) The strain database construction process S19 is a process of storing the strain measured in the strain measurement process S15 for each test piece 100 formed in the test piece forming process S13 in chronological order from the start of forming to the occurrence of fracture, and constructing a strain database.

[0073] <Forming limit analysis step> As shown in FIG. 1, the forming limit analysis step S20 includes an evaluation point sequence setting step S21, a strain distribution acquisition step S23, and a forming limit acquisition step S25.

[0074] (Evaluation point sequence setting process) The evaluation point sequence setting step S21 is a step of setting an evaluation point sequence in each test piece 100 for acquiring the strain distribution in the vicinity of the fracture portion that occurs in each test piece 100 molded in the test piece molding step S13.

[0075] The evaluation point sequence may be set at predetermined intervals along the direction perpendicular to the fractured portion that occurs in the test piece 100, for example, so as to straddle the fractured portion.

[0076] (Strain distribution acquisition process) The strain distribution acquisition step S23 is a step of extracting the strains in the evaluation point sequence set for each test piece 100 in the evaluation point sequence setting step S21 from the strain database, and acquiring the strain distribution in the vicinity of the fractured portion.

[0077] The strain distribution acquisition step S23 may extract, for example, strains at times (time steps) before and after the occurrence of a fracture in the test piece 100 from the strains stored in chronological order at predetermined time intervals from the start of forming to the occurrence of fracture.

[0078] (Forming limit acquisition process) The forming limit acquisition step S25 is a step of determining the forming limit of each test piece 100 based on the strain distribution acquired in the strain distribution acquisition step S23, and calculating the strain path index and equivalent plastic strain at the determined forming limit.

[0079] The determination of the forming limit in the forming limit acquisition step S25 is performed using, for example, the method described in the publicly known document "JP 2023-35533 A." However, the determination of the forming limit is not limited to this, and any method may be used as long as the forming limit is determined using the same criteria for the strain distributions obtained for the test pieces 100 formed using each combination of test pieces 100 and tools (forming dies 11) having different shapes.

[0080] In this embodiment, the forming limit acquisition step S25 calculates a strain increment ratio β, which is expressed by the following formula, as the strain path index.

number

[0081] The strain increment ratio is calculated by extracting the maximum principal strain and the minimum principal strain at the time step determined to be the forming limit and the time step immediately preceding it from the strain database, determining the increments of the maximum principal strain and the minimum principal strain, and then calculating the ratio of these increments according to the above formula.The strain increment ratio may also be calculated as the ratio of the speeds at the forming limits of the maximum principal strain and the minimum principal strain.

[0082] Furthermore, the equivalent plastic strain at the forming limit may be determined based on the maximum principal strain and the minimum principal strain at the forming limit, similar to the strain increment ratio.

[0083] In the forming limit acquisition step S25, the stress triaxiality η expressed by the following formula may be calculated as the strain path index.

number

[0084] Each stress used to calculate the stress triaxiality can be calculated by a finite element method analysis that reproduces the molding of each test piece 100 in the test piece molding step S13.

[0085] As described above, the strain increment ratio and the equivalent plastic strain are not limited to those calculated based on the strain extracted from the strain database in which the strains measured in the strain measurement step S15 are recorded. As with the stress triaxiality, the maximum principal strain and the minimum principal strain occurring in the test piece 100 may be obtained by a finite element method analysis that reproduces the forming of each test piece 100, and the strain increment ratio and the equivalent plastic strain at the forming limit may be calculated.

[0086] <Steps for creating the forming limit surface> As shown in FIG. 1, the forming limit surface creating step S30 includes a forming limit plotting step S31 and a forming limit surface creating step S33.

[0087] (Forming limit plot process) The forming limit plotting step S31 is a step of plotting in a three-dimensional coordinate space the force in the plate thickness direction at the fracture part, the strain increment ratio at the forming limit, and the equivalent plastic strain, which are obtained for each test piece 100 formed in the test piece forming step S13. Here, the three-dimensional coordinate space has three axes, which are the force in the plate thickness direction, the strain increment ratio, and the equivalent plastic strain.

[0088] (Forming limit surface creation process) The forming limit surface creation process S33 is a process of creating a forming limit surface of a metal plate based on a group of plot points of the force in the plate thickness direction at the fracture part, the strain increment ratio at the forming limit, and the equivalent plastic strain plotted in three-dimensional coordinate space.

[0089] The forming limit surface can be created in the forming limit surface creation step S33 by, for example, the following three methods: In the following description, the force in the thickness direction at the fractured part, and the strain increment ratio and equivalent plastic strain at the forming limit are referred to as forming limit data.

[0090] The first method is to first select two adjacent plot points from the group of plot points of the forming limit data obtained for each of multiple test pieces 100 formed using a forming mold 11 of the same shape in a three-dimensional coordinate space in which the forming limit data is plotted.

[0091] Next, from the group of plot points of the forming limit data obtained for each of a plurality of test pieces 100 molded using a molding die 11 having a different shape from the two plot points, one plot point is selected that is closest to the line segment connecting the two selected plot points.

[0092] Then, a triangular plane is created connecting the two selected plot points with one other plot point. This process of creating triangular planes is carried out for all plot points of the forming limit data plotted in the three-dimensional coordinate space. The polygonal surface created by combining the created triangular planes is then used as the forming limit surface.

[0093] The second method for creating a forming limit surface is to first assume a forming limit plane or a forming limit curved surface in a three-dimensional coordinate space, calculate the perpendicular distance between this assumed forming limit plane or curved surface and each plot point of the plot point group of forming limit data plotted in the three-dimensional coordinate space, and then determine the forming limit plane or curved surface so that the sum of squares of the calculated perpendicular distances is minimized.

[0094] The third method for creating a forming limit surface is to determine the forming limit plane or forming limit curved surface in the second method described above so that the sum of squares weighted on the perpendicular distance between the assumed forming limit plane or forming limit curved surface and each plot point of the plot point group of forming limit data is minimized.

[0095] One possible way of weighting is to increase the weight of the vertical distance between the plot points of the forming limit data for the shape or forming path of the forming die 11 for which error is particularly desired to be reduced and the forming limit plane or forming limit curved surface.

[0096] In the second or third method, the forming limit surface may be a combination of a plurality of forming limit planes and / or forming limit curved surfaces. For example, first, in a three-dimensional coordinate space, a forming limit plane or a forming limit curved surface is assumed in each of the regions where the strain path index (strain increment ratio) is negative and positive. Then, for each region, a forming limit plane or a forming limit curved surface is determined so that the sum of squares of the perpendicular distances to each plot point of the plot point group of forming limit data is minimized. The forming limit planes or forming limit curved surfaces determined for each region are then combined to form a forming limit surface. The same applies when creating a forming limit surface so that the sum of squares weighted on the perpendicular distances to the plot points of the forming limit data is minimized.

[0097] As a method other than the above, three adjacent plot points may be selected from the group of plot points of the forming limit data in the three-dimensional coordinate space, and a triangular plane may be generated by connecting the selected three plot points with straight lines. This process may be repeated to generate a polygonal surface consisting of a plurality of triangular planes, which may be used as the forming limit surface.

[0098] <Metal sheet forming limit surface creation system> The metal plate forming limit surface creation system according to this embodiment performs forming tests on metal plates using a plurality of tools with different shapes and various strain paths so as to generate various forces in the plate thickness direction. The metal plate forming limit surface creation system creates a metal plate forming limit surface expressed by the relationship between the force in the plate thickness direction generated in a test piece of the formed metal plate, the strain path index representing the strain path of the formed test piece, and the equivalent plastic strain generated in the formed test piece. The forming limit surface creation system 1 for metal sheets according to this embodiment (hereinafter simply referred to as the "forming limit surface creation system 1") includes a forming test section 10, a forming limit analysis section 20, and a forming limit surface creation section 30, as shown in FIG.

[0099] <Forming Test Section> As shown in FIG. 6, the forming test section 10 includes a forming die 11, a photographing device 13, a strain measuring device 15, a force acquiring device 17 in the plate thickness direction, and a strain database creating device 19.

[0100] (Molding mold) The forming die 11 is a tool having different shapes so that various forces in the thickness direction are generated in the test piece 100 having a predetermined lattice or strain analysis pattern on the surface.

[0101] 2, the molding die 11 has a punch 11a with a spherical tip 11a1, an upper die 11b, and a blank holder 11c. The molding die 11 has a plurality of punches 11a with tip 11a1 having different radii of curvature R (curvature ρ=1 / R), thereby producing a plurality of tools with different shapes.

[0102] In this way, the forming die 11 has punches 11a with tip portions 11a1 of different shapes, which makes it possible to generate various forces in the thickness direction on the test piece 100. As described above, the tip portion 11a1 of the punch 11a is not limited to one with a spherical head shape, but may also be flat (with a radius of curvature R=∞, see FIG. 2(b)).

[0103] (imaging device) The photographing device 13 photographs the surface of each test piece 100 during the process of forming the test piece 100 using a plurality of forming dies 11 with different shapes and various strain paths. In this embodiment, the photographing device 13 photographs the surface of the test piece 100 at predetermined time intervals from the start of forming to the occurrence of fracture.

[0104] (Strain measurement device) The strain measuring device 15 analyzes the image of the surface of each test piece 100 taken by the photographing device 13 and measures the strain occurring in the test piece 100 .

[0105] In this embodiment, the strain measuring device 15 uses a digital image correlation method to measure the maximum principal strain and the minimum principal strain as the strains in two in-plane directions that occur in the test piece 100 during the molding process from the deformation state of the grid or strain analysis pattern on the surface of each test piece 100.

[0106] (Device for acquiring force in the plate thickness direction) The thickness direction force acquisition device 17 obtains the force in the thickness direction at the fracture portion generated in each test piece 100 formed by the forming die 11 .

[0107] In this embodiment, the thickness direction force acquisition device 17 obtains the surface pressure generated at the fractured portion of each molded test piece 100 as the force in the thickness direction. In this case, the thickness direction force acquisition device 17 may measure the surface pressure by placing pressure-sensitive paper 105 between the molding die 11 and each test piece 100 and molding it (see FIG. 2). Alternatively, the thickness direction force acquisition device 17 may perform a finite element method analysis that reproduces the molding of each test piece 100 by the molding die 11, and calculate the surface pressure at the fracture portion of each test piece 100.

[0108] The thickness direction force acquisition device 17 may obtain the thickness direction stress generated at the fractured portion of each test piece 100 as the force in the thickness direction. In this case, the thickness direction force acquisition device 17 calculates the thickness direction stress occurring at the fractured part by finite element method analysis that reproduces the molding of each test piece 100 by the molding die 11. In such finite element method analysis, it is preferable to divide the test piece into elements using solid elements.

[0109] (Strain database construction device) The strain database construction device 19 stores the strain measured by the strain measuring device 15 for each formed test piece 100 in chronological order from the start of forming to the occurrence of fracture, and constructs a strain database.

[0110] <Forming Limit Analysis> As shown in FIG. 6, the forming limit analysis unit 20 includes an evaluation point sequence setting device 21, a strain distribution acquisition device 23, and a forming limit acquisition device 25. The forming limit analysis unit 20 can be, for example, configured by a computer (such as a PC). In this case, each unit of the forming limit analysis unit 20 functions when the CPU of the computer executes a predetermined program.

[0111] (Evaluation point sequence setting device) The evaluation point sequence setting device 21 sets an evaluation point sequence in each test piece 100 for acquiring the strain distribution in the vicinity of a fracture portion that occurs in each molded test piece 100 .

[0112] (Strain distribution acquisition device) The strain distribution acquisition device 23 extracts the strain of the evaluation point sequence set on each test piece 100 by the evaluation point sequence setting device 21 from the strain database, and acquires the strain distribution in the vicinity of the fractured portion.

[0113] (Forming limit acquisition device) The forming limit acquisition device 25 determines the forming limit of each test piece 100 based on the strain distribution acquired by the strain distribution acquisition device 23, and calculates the strain path index and equivalent plastic strain at the determined forming limit. The forming limit acquisition device 25 determines the forming limit for each of a plurality of test pieces 100 with different shapes formed using a plurality of forming dies with different shapes and various strain paths, and calculates the strain path index and equivalent plastic strain at the forming limit.

[0114] In this embodiment, the forming limit acquisition device 25 may determine the forming limit by a method similar to the forming limit acquisition step S25 of the above-described method for creating a forming limit surface of a metal plate.

[0115] In this embodiment, the forming limit acquisition device 25 obtains the strain increment ratio at the forming limit as the strain path index, as explained in the forming limit acquisition step S25.

[0116] Furthermore, the forming limit acquisition device 25 obtains the equivalent plastic strain at the forming limit based on the maximum principal strain and the minimum principal strain at the forming limit.

[0117] The forming limit acquisition device 25 may obtain the stress triaxiality at the forming limit as the strain path index, similarly to the above-described forming limit acquisition step S25. In this case, each stress used to calculate the stress triaxiality may be calculated by a finite element method analysis that reproduces the forming of the test piece 100.

[0118] In addition, the forming limit acquisition device 25 may be a device that, similar to the stress triaxiality, determines the maximum principal strain and minimum principal strain that occur in the test piece by finite element analysis that reproduces the forming of the test piece, and calculates the strain increment ratio and equivalent plastic strain at the forming limit.

[0119] <Forming limit surface creation section> As shown in FIG. 6, the forming limit surface creation unit 30 includes a forming limit plotting device 31 and a forming limit surface creation device 33.

[0120] (Forming limit plotting device) The forming limit plotting device 31 plots the force in the plate thickness direction at the fracture point, the strain path index at the forming limit, and the equivalent plastic strain, which are obtained for each formed test piece 100, in three-dimensional coordinate space.

[0121] Here, the force in the thickness direction at the fractured portion was obtained by the force acquisition device 17 in the thickness direction, and the strain path index and equivalent plastic strain at the forming limit were obtained by the forming limit acquisition device 25.

[0122] (Forming limit surface creation device) The forming limit surface creation device 33 creates a forming limit surface of the metal plate based on a group of plot points of the force in the plate thickness direction at the fracture part, the strain path index at the forming limit, and the equivalent plastic strain, which are plotted in three-dimensional coordinate space by the forming limit plotting device 31.

[0123] The forming limit surface may be created by the forming limit surface creating device 33 by any one of the three methods described in the forming limit surface creating step S33 of the forming limit surface creating method according to the first embodiment.

[0124] <Program for creating forming limit surfaces for metal sheets> The metal plate forming limit surface creation system according to the embodiment of the present invention can be configured as a metal plate forming limit surface creation program that causes the forming limit analysis unit 20 and the forming limit surface creation unit 30, which are configured by a computer, to function.

[0125] That is, the metal plate forming limit surface creation program according to this embodiment has a function of causing a computer to function as the forming limit analysis unit 20 and the forming limit surface creation unit 30 shown in FIG.

[0126] The metal plate forming limit surface creation program according to the first embodiment causes the forming limit analysis unit 20 to function as an evaluation point sequence setting device 21, a strain distribution acquisition device 23, and a forming limit acquisition device 25.

[0127] Furthermore, the metal plate forming limit surface creation program according to this embodiment causes the forming limit surface creation unit 30 to function as a forming limit plotting device 31 and a forming limit surface creation device 33 .

[0128] As described above, according to the method, system, and program for creating a forming limit surface of a metal plate according to this embodiment, the force in the plate thickness direction, the strain path index, and the equivalent plastic strain obtained as indexes of the forming limit can be plotted in three-dimensional coordinate space, and a forming limit surface of the metal plate expressed by the relationship between the force in the plate thickness direction, the strain path index, and the equivalent plastic strain can be created. [Example]

[0129] An experiment was conducted to verify the effects of the present invention, and the results will be described below.

[0130] In the experiment, the forming limit surface of the metal plate was obtained according to the method for creating the forming limit surface of the metal plate according to the embodiment of the present invention described above, following the flow shown in FIG.

[0131] First, in the forming test step S10, the shape of the forming die 11 shown in Fig. 3 was determined as a tool for forming the test piece 100. The forming die 11 was equipped with a punch 11a having a spherical head tip 11a1, an upper die 11b, and a blank holder 11c. In order to generate various forces in the thickness direction on the test piece 100, the radius of curvature R of the spherical head tip 11a1 of the punch 11a was set to four types, namely, R25 mm, R50 mm, R100 mm, and R=∞, as shown in Fig. 4.

[0132] Next, a high-strength steel plate with a tensile strength of 1470 MPa and a thickness of 1.4 mm was used as a test material, and the shape of the test piece 100 was determined. As shown in Fig. 5, the shape of the test piece 100 was a circular test piece 101 with a diameter of φ200 mm, and a test piece 103 with a shape obtained by cutting out this in the width direction. The test piece 103 was shaped such that the width W of the central portion 103b was variously changed.

[0133] Next, a lattice pattern (grid) for strain measurement was transferred onto the surface of the test piece 100 whose shape had been determined.

[0134] Next, the forming die 11 was set in a hydraulic deep drawing test machine, and a test piece 100 was formed. In the experiment, in order to prevent the test piece 100 from flowing in, a blank holder force of 50 tonf was applied by the blank holder 11c, and the punching speed of the punch 11a was set to 5 mm / min. Then, while forming, the surface of the test piece 100 was photographed at time intervals of once per second by an image analysis camera, which is a photographing device (not shown), installed above the forming die 11. Furthermore, as shown in FIG. 3, pressure-sensitive paper 105 was installed between the forming die 11 (punch 11a) and the test piece 100 to measure the surface pressure generated on the test piece 100.

[0135] Next, the images of the surface of the test piece 100 taken during the forming test were analyzed, and the amounts of strain (maximum principal strain and minimum principal strain) generated on the surface of the test piece 100 were measured. The amounts of strain measured during the forming process were then stored in a strain database in chronological order from the start of forming to the occurrence of fracture.

[0136] Next, it was visually determined whether or not a fracture occurred in the test piece 100 during the molding process. If it was determined that no fracture occurred, molding was continued, and the surface of the test piece 100 was photographed, the amount of strain was measured by image analysis, and the results were stored in a strain database. In this way, the surface of the test piece 100 was photographed from the start of molding until fracture occurred, and the amount of strain was measured for each photographed image, and this was continued until it was determined that fracture occurred. When it was determined that a break had occurred, the pressure-sensitive paper 105 placed between the molding die 11 and the test piece 100 was removed, and the surface pressure at the break was measured.

[0137] Subsequently, it was determined whether or not the molding test had been carried out for all the test piece shapes. When it was determined that the forming test had been performed for all the shapes of the test piece 100, it was determined whether or not the forming test had been performed for all the shapes of the prepared punch 11a. In this way, the above forming test was performed for all the shapes of the test piece and the tool (shape of the punch 11a). Then, when it is determined that the forming test has been performed for all the tool shapes, the forming test step S10 is completed.

[0138] After the forming test step S10 was completed, in the forming limit analysis step S20, a forming limit analysis was performed using the strain database constructed in the forming test step S10.

[0139] First, a series of evaluation points for acquiring strain distribution was set in the vicinity of a fractured portion that occurred in the molded test piece 100. Next, for the set evaluation point sequence, time series data of maximum principal strain and minimum principal strain were extracted from the strain database, and the strain distribution was obtained.

[0140] The forming limit of the test piece 100 was determined based on the acquired strain distribution, and the strain path index and equivalent plastic strain at the determined forming limit were determined as the forming limit strain. This operation was performed on the test piece 100 formed in each forming test in which the tip 11a1 of the punch 11a and the shape of the test piece 100 were changed, and the forming limit strain (strain increment ratio and equivalent plastic strain) was determined.

[0141] Fig. 8 is a graph showing the transition of the maximum principal strain and the minimum principal strain generated in the test piece 100 formed under different forming conditions (shape of the punch 11a, shape of the test piece 100) from the start of forming to the forming limit, i.e., the deformation path. Note that the ● mark in Fig. 8 represents the forming limit.

[0142] In Figure 8, for both deformation path a and deformation path b, the slope of the curve gradually changes as forming progresses, and then remains constant. Here, the slope of each curve is the ratio of the maximum principal strain increment dε1 to the minimum principal strain increment dε2, and is the reciprocal of the strain increment ratio β, which represents the strain path. Therefore, for both deformation path a and deformation path b, the strain path changes from the start of forming to the forming limit, and then the test piece 100 is formed along a predetermined strain path.

[0143] In addition, the strain increment ratio β at the forming limit of deformation path a is -0.34, and the strain increment ratio at the forming limit of deformation path b is 0.00. This shows that the test piece 100 is formed through different strain paths for deformation path a and deformation path b.

[0144] Table 1 shows the results of the surface pressure (force in the thickness direction) generated on the test piece 103 and the forming limit strain (strain increment ratio and equivalent plastic strain) obtained for each shape of the test piece 103 and the shape of the forming die 11.

[0145] [Table 1]

[0146] After the forming limit analysis step S20 was completed, a forming limit surface was created in the forming limit surface creation step S30.

[0147] In the forming limit surface creation step S30, first, the forming limit data (force in the plate thickness direction at the fracture part, strain increment ratio and equivalent plastic strain at the forming limit) obtained for each shape of the test piece 100 and the shape of the forming mold 11 were plotted in three-dimensional coordinate space.

[0148] Next, a forming limit surface was determined that approximated the group of plotted points in the three-dimensional coordinate space. In this example, forming limit planes expressed by the following formula (1) were assumed for the negative and positive strain increment ratio regions, respectively.

[0149]

number

[0150] Then, the coefficients in formula (1) were determined for the forming limit plane A in the positive region and the forming limit plane B in the negative region so that the sum of squares of the perpendicular distances between the assumed forming limit plane and each plot point of the forming limit data was minimized. In this way, the forming limit plane A and the forming limit plane B whose coefficients in formula (1) were determined were obtained as the forming limit surfaces.

[0151] Table 2 shows the coefficients a, b, c, and d in equation (1) for the determined forming limit plane A and forming limit plane B. Furthermore, Fig. 9 shows a group of plots of forming limit data (force in the thickness direction at the fracture part, strain increment ratio at the forming limit, and equivalent plastic strain), as well as forming limit plane A and forming limit plane B created based on the determined coefficients.

[0152] [Table 2]

[0153] As described above, according to the present invention, it was possible to create a forming limit surface expressed by the relationship between the force in the thickness direction (surface pressure), the strain path index (strain increment ratio), and the equivalent plastic strain, as shown in Figure 9. [Explanation of symbols]

[0154] 1. Forming limit surface creation system 10. Forming Test Section 11 Molding mold 11a Punch 11a1 Tip 11b Upper die 11c Wrinkle holder 13 Imaging equipment 15 Strain measurement device 17. Plate thickness direction force acquisition device 19 Strain database construction device 20 Forming Limit Analysis Section 21 Evaluation point sequence setting device 23 Strain distribution acquisition device 25 Forming limit acquisition device 30 Forming limit surface creation section 31 Forming limit plotting device 33 Forming limit surface creation device 41 Molding test result input section 43 Forming Limit Analysis Section 45 Forming limit surface creation section 100 test specimens 101 Test piece 103 Test Pieces 103a Notch 103b Central part 105 Pressure-sensitive Paper 110 test specimens 120 Press molding die 121 V-bending punch 121A V-bending punch 121a Tip 121b Gap forming part 123 Upper die 125 Wrinkle Holder 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 Dummy seat

Claims

1. A method for obtaining the forming limit of a metal plate, characterized by conducting a forming test of a metal plate using a plurality of tools of different shapes that generate various forces in the plate thickness direction and various strain paths, and determining the force in the plate thickness direction generated in a test piece of the formed metal plate, a strain path index representing the strain path of the formed test piece, and the equivalent plastic strain generated in the formed test piece as indicators of the forming limit of the metal plate.

2. A forming limit surface creation method for a metal plate, which performs a forming test of a metal plate using a plurality of tools having different shapes that generate various forces in the plate thickness direction and various strain paths, and creates a forming limit surface of the metal plate that is expressed by the relationship between the force in the plate thickness direction generated in a test piece of the formed metal plate, a strain path index that represents the strain path of the formed test piece, and an equivalent plastic strain generated in the formed test piece, The method includes a forming test step, a forming limit analysis step, and a forming limit surface creation step, The molding test step includes: a test piece preparation step of preparing a plurality of test pieces having different shapes and having a predetermined lattice or strain analysis pattern applied to the surface; a test piece forming step of forming each test piece using a plurality of tools having different shapes and various strain paths while photographing the surface of the test piece; a strain measurement step of analyzing the photographed images of the surfaces of the test pieces and measuring strains occurring in the test pieces; a thickness direction force acquisition step of determining a thickness direction force at a fracture portion occurring in each of the molded test pieces; a strain database construction step of storing the strains measured in the strain measurement step for each of the formed test pieces in chronological order from the start of forming to the occurrence of fracture, and constructing a strain database; The forming limit analysis step includes: an evaluation point sequence setting step of setting an evaluation point sequence in each of the molded test pieces to acquire a strain distribution in the vicinity of the fracture portion generated in each of the molded test pieces; a strain distribution acquisition step of extracting the strain of the evaluation point sequence set for each of the test pieces from the strain database and acquiring a strain distribution in the vicinity of the fractured portion; a forming limit acquisition step of determining a forming limit of each of the test pieces based on the acquired strain distribution, and calculating a strain path index and an equivalent plastic strain at the determined forming limit, The forming limit surface creation step includes: a forming limit plotting step of plotting the force in the plate thickness direction at the fracture portion, the strain path index at the forming limit, and the equivalent plastic strain, which are obtained for each of the formed test pieces, in a three-dimensional coordinate space; and a forming limit surface creation step of creating a forming limit surface of the metal plate based on a group of plot points of the force in the plate thickness direction at the fracture part, and the strain path index and equivalent plastic strain at the forming limit, plotted in the three-dimensional coordinate space.

3. 3. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the plate thickness direction force acquisition step, the force in the plate thickness direction is obtained as the surface pressure generated at the fracture portion of each of the formed test pieces.

4. 4. The method for creating a forming limit surface of a metal plate according to claim 3, wherein the surface pressure is measured by placing pressure-sensitive paper between the tool and each of the test pieces during the test piece forming process, or is calculated by finite element method analysis that reproduces the forming of each of the test pieces during the test piece forming process.

5. 3. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the plate thickness direction force acquisition step, the plate thickness direction stress generated at the fracture portion of each of the test pieces formed in the test piece forming step is obtained as the plate thickness direction force.

6. 6. The method for creating a forming limit surface of a metal plate according to claim 5, wherein the stress in the plate thickness direction is calculated by a finite element method analysis that reproduces the forming of each of the test pieces in the test piece forming step.

7. 7. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the forming limit acquisition step, a strain increment ratio expressed by the following formula is calculated as the strain path index: [Equation 1]

8. 7. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the forming limit acquisition step, a stress triaxiality expressed by the following formula is calculated as the strain path index: [Equation 2]

9. 7. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the forming limit surface creation step, a polygonal surface is created that is made up of a plurality of triangular planes that connect two adjacent plot points among the plot point groups for the plurality of test pieces formed using the tool having the same shape, and one plot point that is closest to the line segment connecting the two plot points among the plot point groups for the plurality of test pieces formed using the tool having a shape different from that of the two plot points.

10. 7. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the forming limit surface creation step, a forming limit plane or a forming limit curved surface is assumed, the sum of squares of the perpendicular distances between the assumed forming limit plane or the forming limit curved surface and each plot point of the plot point group in the three-dimensional coordinate space is calculated, and the forming limit plane or the forming limit curved surface is determined so that the calculated sum of squares is minimum.

11. 7. The method for creating a forming limit surface of a metal plate according to claim 2, wherein in the forming limit surface creation step, a forming limit plane or a forming limit curved surface is assumed, a sum of squares weighted on a perpendicular distance between the assumed forming limit plane or the forming limit curved surface and each plot point of the group of plot points in the three-dimensional coordinate space is calculated, and the forming limit plane or the forming limit curved surface is determined so that the calculated sum of squares is minimized.

12. 11. The method for creating a forming limit surface of a metal plate according to claim 10, wherein in the forming limit surface creation step, the forming limit surface is created by combining a plurality of the forming limit planes and / or the forming limit curved surfaces.

13. 12. The method for creating a forming limit surface of a metal plate according to claim 11, wherein in the forming limit surface creation step, the forming limit surface is created by combining a plurality of the forming limit planes and / or the forming limit curved surfaces.

14. A forming limit surface creation system for a metal plate, which performs a forming test of a metal plate using a plurality of tools having different shapes that generate various forces in the plate thickness direction and various strain paths, and creates a forming limit surface of the metal plate that is expressed by the relationship between the force in the plate thickness direction that occurs in a test piece of the formed metal plate, a strain path index that represents the strain path of the formed test piece, and an equivalent plastic strain that occurs in the formed test piece, The apparatus includes a forming test section, a forming limit analysis section, and a forming limit surface creation section, The molding test section a plurality of tools having different shapes for forming a plurality of test pieces having different shapes, each of which has a predetermined lattice or strain analysis pattern applied to its surface, so that various forces in the thickness direction are generated in each of the test pieces; an imaging device that images the surface during the process of forming each of the test pieces using multiple tools and various strain paths; a strain measuring device that analyzes the captured image of the surface of each of the test pieces and measures strain occurring in each of the test pieces; a thickness direction force acquisition device for determining a thickness direction force at a fracture portion generated in each of the molded test pieces; a strain database construction device that stores the strain measured by the strain measuring device for each of the formed test pieces in chronological order from the start of forming to the occurrence of fracture, and constructs a strain database; The forming limit analysis unit an evaluation point sequence setting device that sets an evaluation point sequence on the test piece to acquire strain distribution in the vicinity of the fracture portion generated in each of the molded test pieces; a strain distribution acquisition device that extracts the strain of the evaluation point sequence set on each of the test pieces from the strain database and acquires the strain distribution in the vicinity of each of the fractured portions; a forming limit acquisition device that determines a forming limit of each of the test pieces based on the acquired strain distribution, and calculates a strain path index and an equivalent plastic strain at the determined forming limit, The forming limit surface creation unit a forming limit plotting device that plots the force in the plate thickness direction at the fracture portion, the strain path index at the forming limit, and the equivalent plastic strain, which are obtained for each of the formed test pieces, in a three-dimensional coordinate space; and a forming limit surface creation device that creates a forming limit surface of the metal plate based on a group of plot points of the force in the plate thickness direction at the fracture part, and the strain path index and equivalent plastic strain at the forming limit, plotted in the three-dimensional coordinate space.

15. A forming limit surface creation program for a metal plate, which creates a forming limit surface of the metal plate expressed by the relationship between a force in the plate thickness direction generated in a test piece of the metal plate formed in a forming test of the metal plate using a plurality of tools having different shapes so as to generate various forces in the plate thickness direction and various strain paths, a strain path index, and an equivalent plastic strain, A forming limit surface creation program for a metal plate, comprising a function of causing a computer to execute the forming limit analysis unit and the forming limit surface creation unit of the metal plate forming limit surface creation system according to claim 14.

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