Method for determining forming limit strain

Abstract

This method for determining forming limit strain comprises performing an extending-out forming test conforming to ISO 12004-2 standard until a fracture part 11 is generated in a test piece 10 of a sheet material. The extending-out forming test involves: continuously photographing the test piece 10 in time series; calculating data related to a temporal change of the difference ΔVmax in maximum major strain speed between two gauge lengths L1, L2, on the basis of images of the fracture part 11 of the photographed test piece 10; and, by presuming that the time when the difference has increased to a prescribed threshold ΔVth is a local constriction onset time Tth in the calculated temporal change data of the difference ΔVmax, determining the maximum major strain Emax and the minimum major strain Emin at the local constriction onset time Tth as the maximum major strain and the minimum major strain of a forming limit strain on the sheet material.

Description

How to determine the forming limit strain

[0001] The present technology relates to a method for determining forming limit strain.

[0002] The use of aluminum alloy sheets is expanding in order to reduce the weight of transportation equipment. However, aluminum alloy sheets have lower ductility than steel sheets, making them prone to cracking (fracture) when press-formed into vehicle body panels, etc. If a fracture occurs, the number of times the forming die needs to be modified increases, so there is an increasing need for fracture prediction through simulation.

[0003] Conventionally, a method for determining the forming limit curve (FLC) standardized by ISO (ISO 12004-2 standard) has been known for predicting fracture in press forming. However, there are metals to which this method cannot be applied. For example, in 5000 series aluminum alloys, strain generated during tensile deformation does not occur uniformly and simply, but occurs in a complex manner due to non-uniform deformation. The ISO standard method cannot be applied to metals that exhibit such non-uniform deformation behavior.

[0004] On the other hand, Non-Patent Document 1 describes a method for determining the forming limit strain (threshold) (hereinafter referred to as the LBF method) that can be applied to metals that exhibit non-uniform deformation behavior. If the forming limit strain can be determined in advance, it is possible to predict that fracture will occur when it is exceeded.

[0005] Key Engineering Materials, (Switzerland), 2013, Vol.549, pp.397-404

[0006] (Problem to be Solved by the Invention) However, the LBF method of Non-Patent Document 1 may have low accuracy. For example, when applied to a metal that exhibits uniform deformation behavior (a metal in which strain occurs simply and uniformly, such as a 6000 series aluminum alloy), the forming limit strain may be determined to be excessively large. As a result, during press forming, fracture may occur before the determined forming limit strain is exceeded.

[0007] This technology was developed based on the above-mentioned circumstances, and aims to realize a method for determining forming limit strain with high accuracy that is applicable to a wide variety of metals.

[0008] (Means for solving the problem) A method for determining a forming limit strain according to the present technology is a method for determining a forming limit strain, which is a threshold value of a forming limit in press forming of a metal plate material, and includes the steps of: performing a stretch forming test in accordance with ISO 12004-2 standard on a test piece of the plate material until a fracture occurs in the test piece; photographing the test piece continuously in time series in the stretch forming test; in the photographed images of the fracture portion of the test piece, setting a distance between a first gauge point and a second gauge point separated by the fracture portion as a first gauge length; setting a distance between a third gauge point and a fourth gauge point separated by the fracture portion as a second gauge length; and adjusting the distances of the third gauge point and the fourth gauge point so that the second gauge length is greater than the first gauge length. a position is set, and data on the change over time of the difference between the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length is calculated based on the photographed image of the fracture portion of the test piece, and the time at which the difference in the calculated data on the change over time of the difference increases to a predetermined threshold is regarded as the time at which local necking occurs, and the maximum principal strain at the first gauge length or the maximum principal strain at the second gauge length at the time at which local necking occurs is determined to be the maximum principal strain of the forming limit strain of the plate material, and the minimum principal strain at the first gauge length or the minimum principal strain at the second gauge length at the time at which local necking occurs is determined to be the minimum principal strain of the forming limit strain of the plate material.

[0009] The predetermined threshold value may be set by approximating the variation in data of the difference between the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length with a normal distribution.

[0010] Furthermore, when the average value of the differences obtained by approximating the normal distribution is μ and the standard deviation of the differences is σ, the predetermined threshold value may be set to μ+3σ.

[0011] Furthermore, in the stretch forming test, when the test piece is continuously photographed in time series, the images may be taken from a plurality of observation points, and data on the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length may be obtained based on images of the fracture portion of the test piece photographed at the plurality of observation points.

[0012] The punch on which the test piece is placed in the stretch forming test may have a flat placement surface.

[0013] The metal may also be an aluminum alloy.

[0014] (Effects of the Invention) According to the present technology, a method for determining forming limit strain with high accuracy can be realized, which is applicable to a wide variety of metals.

[0015] Schematic diagram showing an example of a stretch forming test (Nakajima method) Schematic diagram showing an example of a stretch forming test (Marciniak method) Plan view showing the stretched state of the test specimen (uniaxial tension, state 2) Plan view showing the stretched state of the test specimen (plane strain, state 1) Plan view showing the stretched state of the test specimen (non-equiaxial tension, state 3) Plan view showing the stretched state of the test specimen (equibiaxial tension, state 4) Schematic diagram showing the forming limit line Schematic diagram showing the digital image correlation method Image showing uniform deformation of the test specimen (no necking) (uniaxial tension) Image showing the test specimen just before fracture (with necking) (uniaxial tension) Image showing the test specimen after fracture (uniaxial tension) Plan view showing two gauge lengths before fracture of the test specimen Plan view showing two gauge lengths after fracture of the test specimen Schematic diagram showing the time changes in minimum principal strain, maximum principal strain, and maximum principal strain rate At maximum principal strain rate for two gauge lengths Data on the change over time in the difference in maximum principal strain rates between two gauge lengths (uniaxial tension) Enlarged view of Figure 8 Data on the change over time in the difference in maximum principal strain rates between two gauge lengths (uniaxial tension) Enlarged view of Figure 10A Enlarged view of Figure 5A at the first gauge length (uniform deformation, no necking) Enlarged view of Figure 5A at the second gauge length (uniform deformation, no necking) Enlarged view of Figure 5B at the first gauge length (necking occurs) Enlarged view of Figure 5B at the second gauge length (necking occurs) Data on the change over time in the difference in maximum principal strain rates between two gauge lengths (uniaxial tension) Data on the change over time in the difference in maximum principal strain rates between two gauge lengths (plane strain) Data on the change over time in the difference in maximum principal strain rates between two gauge lengths (equibiaxial tension) Example of determined forming limit strain (6000 series aluminum alloy) Example of determined forming limit strain (5000 series aluminum alloy)

[0016] <Embodiment> A method for determining the forming limit strain, which is the threshold value (reference value) of the forming limit in press forming of a metal plate, will be described with reference to Figures 1 to 17. Some figures show the X-axis, Y-axis, and Z-axis, and each axis direction is drawn so as to be a common direction in each figure. Furthermore, the Z-axis direction is defined as the up-down direction, but this direction is merely defined for convenience and should not be interpreted in a limiting sense.

[0017] The method for determining the forming limit strain according to this embodiment (hereinafter referred to as the G.L. method) roughly includes the steps of: conducting a bulge forming test using a test piece 10 (S10); photographing an image of the test piece 10 during the bulge forming test (S20); calculating a difference ΔVmax in maximum principal strain rates at two gauge lengths (S30); determining a time Tth at which local necking occurs using the calculated difference ΔVmax in maximum principal strain rates (S40); and determining a minimum principal strain Emin and a maximum principal strain Emax at the determined time Tth at which local necking occurs (S50). According to the G.L. method, the minimum principal strain Emin, which is the minimum value of strain, and the maximum principal strain Emax, which is the maximum value of strain, generated in a metal plate material subjected to a load during press forming can be accurately determined in advance as reference values ​​for the forming limit strain. As a result, it becomes possible to predict with high accuracy whether or not a break will occur in the metal plate material when the reference value is exceeded during press forming. Steps S10 to S50 will now be described in detail.

[0018] The stretch forming test step S10 is a process of performing a stretch forming test on a metal plate test piece 10 in accordance with the ISO 12004-2 standard until a fracture 11 occurs in the test piece 10. The ISO 12004-2 standard specifies the Nakajima method shown in FIG. 1A and the Marciniak method shown in FIG. 1B. In the Nakajima method shown in FIG. 1A, the mounting surface 20A of the punch 20 on which the test piece 10 is placed is approximately hemispherical. On the other hand, in the Marciniak method shown in FIG. 1B, the mounting surface 120A of the punch 120 on which the test piece 10 is placed is flat (planar). In addition, in the Marciniak method, a drive plate 24 is interposed between the mounting surface 120A and the test piece 10. The main difference between the two methods is the shape of the mounting surfaces 20A and 120A, and the basic content of the implementation step S10 is the same for both methods.

[0019] 1A and 1B, in step S10 of the bulge forming test, the end 10A of the test piece 10 is sandwiched between an upper mold 22 and a blank holder 23 from above and below (in the Z-axis direction) to support the test piece 10. In this state, punches 20, 120 press between the end 10A of the test piece 10. The punches 20, 120 and the drive plate 24 are configured so that the test piece 10 is subjected to a load by the pressing force, and the pressing force (load) increases over time. As the load increases, strain occurs in the test piece 10, and as the strain increases, localized necking occurs in the test piece 10. Immediately after the localized necking occurs, the localized necking becomes a fracture portion 11 (see FIGS. 5A to 5C).

[0020] Generally, the forming limit strain of a metal sheet depends on the type of metal, the thickness, and the deformation region of the sheet. Therefore, it is preferable to perform a stretch forming test according to the object whose forming limit strain is to be determined. The test piece 10 according to this embodiment is, for example, a 5000 series aluminum alloy (an example of a metal exhibiting non-uniform deformation behavior) or a 6000 series aluminum alloy (an example of a metal exhibiting uniform deformation behavior), and has a thickness of 1.0 mm. The deformation region of the test piece 10 subjected to load is one of three cases: uniaxial tension (state 2) shown in FIG. 2A , plane strain (state 1) shown in FIG. 2B , or equibiaxial tension (state 4) shown in FIG. 2D . However, the type of metal, thickness, and deformation region of the test piece 10 are not limited to these and can be appropriately selected according to the object whose forming limit strain is to be determined.

[0021] Here, the deformation region of the test specimen 10 will be described. Uniaxial tension (State 1) and plane strain (State 2) are states in which the test specimen 10 is stretched in the Y-axis direction (first direction), as shown in Figures 2A and 2B, respectively. At this time, when the load in the Y-axis direction exceeds a predetermined magnitude, the test specimen 10 contracts in the X-axis direction (second direction) intersecting the Y-axis direction. A state in which the test specimen 10 is stretched in the Y-axis direction and contracted in the X-axis direction is considered uniaxial tension (Figure 2A), while a state in which the test specimen 10 is stretched in the Y-axis direction but not in the X-axis direction is considered plane strain (Figure 2B). Non-equiaxial tension (State 3) and equibiaxial tension (State 4) are states in which the test specimen 10 is stretched in both the Y-axis direction and the X-axis direction, as shown in Figures 2C and 2D, respectively. Equibiaxial tension is a state in which the test specimen 10 is stretched in both the Y-axis direction and the X-axis direction, and the degree of stretching in the Y-axis direction and the X-axis direction is close to being equal (Figure 2D).

[0022] The relationship between the strain region of the test piece 10 and the minimum principal strain Emin and the maximum principal strain Emax, which are reference values ​​of the forming limit strain, is shown by a forming limit line as shown in Fig. 3. Fig. 3 is a schematic diagram showing an image of the forming limit line of a certain metal plate material.

[0023] In the plane strain state (state 2), the test piece 10 neither expands nor contracts in the X-axis direction, and as shown in Figure 3, the minimum principal strain Emin is zero (measured close to zero), and the maximum principal strain Emax is, for example, +Ex2. In the uniaxial tension state (state 1), the test piece 10 contracts in the X-axis direction, and the minimum principal strain Emin is, for example, -En1, and the maximum principal strain Emax is, for example, +Ex1. In the non-equibiaxial tension state (state 3), the test piece 10 expands in the X-axis and Y-axis directions, and the minimum principal strain Emin is, for example, +En2, and the maximum principal strain Emax is, for example, +Ex3. In addition, in the state of equibiaxial tension (state 4), the test piece 10 is stretched equally in the X-axis direction and the Y-axis direction, and the minimum principal strain Emin is, for example, +En3, and the maximum principal strain Emax is, for example, +Ex4.

[0024] Next, the image capturing step S20 and the calculation step S30 of the difference ΔVmax in the maximum principal strain rates at the two gauge lengths using the captured images will be described. These steps S20 and S30 use the so-called digital image correlation (DIC) method. More specifically, as shown in FIG. 4 , the surface of the test piece 10 is sprayed with the coating liquid 31 in advance (at least before the load is applied in the stretch forming test step S10). Then, the surface of the test piece 10, onto which the coating liquid 31 with a random pattern of fine dots has been applied, is continuously photographed in chronological order during the stretch forming test step S10. The surface of the test piece 10 is simultaneously photographed from multiple observation points, for example, by two cameras 33.

[0025] 5A to 5C are example images of a fractured portion 11 of a test specimen 10 (6000 series aluminum alloy, plate thickness 1.0 mm). When a load is applied to the test specimen 10 and the load increases over time, strain occurs in the test specimen 10 (FIG. 5A). When the strain in the test specimen 10 increases to a certain threshold, local necking occurs (FIG. 5B). Immediately after the local necking occurs, the local necking becomes a fractured portion 11 (FIG. 5C). With the digital image correlation method, the displacement, strain, and strain rate on the surface of the test specimen 10 can be measured (calculated) in a non-contact manner based on such images taken by multiple cameras 33.

[0026] 6A and 6B are schematic diagrams showing images of two gauge lengths before and after the occurrence of a fracture 11 in the test piece 10. In the image of the test piece 10, as shown in FIG. 6B, the distance between a first gauge point P1 and a second gauge point P2, which are separated by the fracture 11 of the test piece 10, is defined as a first gauge length L1. Furthermore, the distance between a third gauge point P3 and a fourth gauge point P4, which are separated by the fracture 11, is defined as a second gauge length L2. The positions of the third gauge point P3 and the fourth gauge point P4 are set so that the second gauge length L2 is greater than the first gauge length L1.

[0027] In an image before the fracture 11 occurs in the test piece 10, the gauge lengths L1 and L2 are smaller by the deformation amounts ΔL1 and ΔL2, respectively, as shown in Fig. 6A. Therefore, the strain at the first gauge length L1 is ΔL1 / (L1-ΔL1), and the strain at the second gauge length L2 is ΔL2 / (L2-ΔL2).

[0028] Furthermore, for the strain at each gauge length L1, L2, the minimum principal strain Emin and the maximum principal strain Emax are calculated, as shown in Fig. 7. Furthermore, based on the change in the maximum principal strain Emax over time, the maximum principal strain rate Vmax1 at the first gauge length L1 and the maximum principal strain rate Vmax2 at the second gauge length L2 are calculated. By using the digital image correlation method, these values ​​can be calculated efficiently with high accuracy.

[0029] 8 and 9 show data on the time change of the maximum principal strain rate Vmax calculated for the test specimen 10 (a 6000 series aluminum alloy, a plate thickness of 1.0 mm, and a deformation region of uniaxial tension (state 1)). The data show the case where the first gauge length L1 is 1 mm and the second gauge length L2 is 2 mm. As shown in FIG. 9, the difference between the maximum principal strain rate Vmax1 at the first gauge length L1 and the maximum principal strain rate Vmax2 at the second gauge length L2 increases significantly from a certain time. Therefore, when the difference ΔVmax between the maximum principal strain rates at the two gauge lengths L1 and L2 is calculated (calculation step S30), the calculated difference ΔVmax increases significantly from a certain time Tth, as shown in FIGS. 10A and 10B.

[0030] The present inventors have found that, when magnifying and observing the image of the portion of the test specimen 10 where the fracture 11 occurs at time Tth, at which the difference ΔVmax between the maximum principal strain rates at the two gauge lengths L1 and L2 increases rapidly, the time change (increment) of the maximum principal strain Emax differs between the two gauge lengths L1 and L2, as shown in Figures 11A, 11B, 12A, and 12B. More specifically, the inventors have found that, while there is no difference between the images of the two gauge lengths L1 and L2 shown in Figures 11A and 11B before the occurrence of local necking, there is a difference in the increment of the maximum principal strain Emax between the images of the two gauge lengths L1 and L2 shown in Figures 12A and 12B after the occurrence of local necking (immediately before the occurrence of the fracture 11). Based on this, it has been found that the time Tth can be regarded as the "time of occurrence of local necking" immediately before the occurrence of the fracture 11.

[0031] As described above, the local necking occurrence time Tth is the time when the difference ΔVmax between the maximum principal strain rates at the two gauge lengths L1 and L2 increases rapidly. However, the difference ΔVmax in actual data contains a certain degree of variation, as shown in Figures 10B and 13. For this reason, if the time when the difference ΔVmax exceeds 0 is determined as the local necking occurrence time Tth, there is a concern that the local necking occurrence time Tth may not be determined correctly.

[0032] Therefore, in step S40 of determining the local necking occurrence time according to this embodiment, the time when the difference ΔVmax between the maximum principal strain rates at the two gauge lengths L1 and L2 increases to a predetermined threshold ΔVth is set as the local necking occurrence time Tth, as shown in Fig. 13 . Here, the threshold ΔVth is preferably determined by approximating the variation in data of the difference ΔVmax near zero using a normal distribution. More specifically, when the mean value of the data of the difference ΔVmax near zero obtained by approximating using a normal distribution is μ and the standard deviation is σ, the threshold ΔVth is preferably set to (μ + 3σ). In this way, the threshold ΔVth can be determined more accurately, and the local necking occurrence time Tth can be determined with higher precision. When calculating the mean value μ and the standard deviation σ by approximating the normal distribution, the range of data near zero for the difference ΔVmax is, for example, up to Tx / 2, where Tx is the time when the fracture 11 occurs in the test piece 10 (see FIG. 10A).

[0033] The data shown in Figures 8 to 13, the threshold value ΔVth, and the local necking occurrence time Tth determined thereby apply to the case where the extension state of the test specimen 10 is uniaxial tension (State 1). Similar steps are performed when the extension state is plane strain (State 2) and equibiaxial tension (State 4). As a result, as shown in Figures 14 and 15, the difference ΔVmax between the maximum principal strain rates at the two gauge lengths L1 and L2, the threshold value ΔVth (= μ + 3σ), and the local necking occurrence time Tth are calculated for the cases of plane strain (State 2) and equibiaxial tension (State 4), respectively.

[0034] Next, the maximum principal strain Emax at the first gauge length L1 or the maximum principal strain Emax at the second gauge length L2 at the time Tth when local necking occurs determined in the above-mentioned determination step S40 is determined as the maximum principal strain, and the minimum principal strain Emax at the first gauge length L1 or the minimum principal strain Emax at the second gauge length L2 is determined as the minimum principal strain (FIG. 7, step S50 for determining the minimum principal strain Emin and the maximum principal strain Emax at the time Tth when local necking occurs).In this way, the minimum principal strain Emin and the maximum principal strain Emax (growth limit strain) of the test specimen 10 in each of the extension states of uniaxial tension (state 1), plane strain (state 2), and equibiaxial tension (state 4) are determined as shown in Example 1 (G.L. method) in FIG.

[0035] Comparative Example 1 in Figure 16 shows the minimum principal strain Emin and maximum principal strain Emax determined by the conventional LBF method for the same test specimen 10 (6000 series aluminum alloy, plate thickness 1.0 mm) as in Example 1. In the case of Comparative Example 1 (LBF method), when applied to a metal exhibiting uniform deformation behavior, such as a 6000 series aluminum alloy, the minimum principal strain Emin and maximum principal strain Emax are determined to be excessively large. Therefore, during press forming, fracture may occur before the determined forming limit strain is exceeded. In contrast, according to Example 1 (G.L. method), as shown in Figure 16, it was confirmed that the minimum principal strain Emin and maximum principal strain Emax are not excessively large as in Comparative Example 1 (LBF method), and can be determined with high accuracy.

[0036] 17 shows the minimum principal strain Emin and the maximum principal strain Emax determined by the G.L. method (Example 2) and the LBF method (Comparative Example 2) for the test specimen 10 made of a 5000 series aluminum alloy and having a plate thickness of 1.0 mm. It was confirmed that in the case of a metal that exhibits non-uniform deformation behavior such as a 5000 series aluminum alloy, the minimum principal strain Emin and the maximum principal strain Emax can be determined with high accuracy regardless of which method is used (in both Example 2 and Comparative Example 2).

[0037] As described above, the G.L. method according to this embodiment can determine the forming limit strain with high accuracy for both metals exhibiting uniform deformation behavior (e.g., 6000 series aluminum alloys) and metals exhibiting non-uniform deformation behavior (e.g., 5000 series aluminum alloys). The G.L. method can determine the forming limit strain with high accuracy regardless of the type of aluminum alloy (e.g., 5000 series or 6000 series) expected to be used as a lightweight material for transportation equipment. Furthermore, the G.L. method can determine the forming limit strain with high accuracy not only for aluminum alloys but also for various types of metals.

[0038] The inventors of the present application also performed both the Nakajima method shown in FIG. 1A and the Marciniak method shown in FIG. 1B in the bulge forming test implementation step S10 of the G.L. method and found that the latter method is preferable because it can more accurately determine the local necking onset time Tth. The reason the Marciniak method (where the installation surface 120A of the punch 120 is planar) is preferable is because data obtained by the Marciniak method are more suitable for normal distribution approximation when determining the threshold value ΔVth in the local necking onset time Tth determination step S40. Therefore, the data disclosed in this specification are data obtained when the Marciniak method is used in implementation step S10.

[0039] 10...Test piece, 20, 120...Punch, 20A, 120A...Placement surface, 11...Fracture portion, Emax...Maximum principal strain, Emin...Minimum principal strain, L1...First gauge length, L2...Second gauge length, P1...First gauge point, P2...Second gauge point, P3...Third gauge point, P4...Fourth gauge point, Tth...Time at which local necking occurs, ΔVmax...Difference in maximum principal strain rate, ΔVth...Threshold value, Vmax1...Maximum principal strain rate at first gauge length, Vmax2...Maximum principal strain rate at second gauge length

Claims

1. A method for determining a forming limit strain, which is a threshold value for the forming limit in press forming of a metal plate material, comprising: conducting a stretch forming test in accordance with ISO 12004-2 standard on a test piece of the plate material until a fracture occurs in the test piece; continuously photographing the test piece in time series during the stretch forming test; in the photographed images of the fracture part of the test piece, setting the distance between a first gauge length and a second gauge length, which are separated by the fracture part, as a first gauge length; setting the distance between a third gauge length and a fourth gauge length, which are separated by the fracture part, as a second gauge length, and setting the positions of the third gauge length and the fourth gauge length so that the second gauge length is greater than the first gauge length; and calculating data on the change over time of the difference between the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length, based on the photographed images of the fracture part of the test piece. A method for determining a forming limit strain, comprising: determining, in data on the calculated change in the difference over time, the time at which the difference increases to a predetermined threshold as the time at which local necking occurs; determining the maximum principal strain at the first gauge length or the maximum principal strain at the second gauge length at the time at which local necking occurs as the maximum principal strain of the forming limit strain of the plate material; and determining the minimum principal strain at the first gauge length or the minimum principal strain at the second gauge length at the time at which local necking occurs as the minimum principal strain of the forming limit strain of the plate material.

2. A method for determining a forming limit strain as described in claim 1, wherein the predetermined threshold value is set by approximating the variation in data of the difference between the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length with a normal distribution.

3. A method for determining a forming limit strain according to claim 2, wherein the predetermined threshold value is set to μ + 3σ, where μ is the average value of the difference obtained by approximating the normal distribution, and σ is the standard deviation of the difference.

4. A method for determining a forming limit strain according to any one of claims 1 to 3, wherein, in the stretch forming test, when the test piece is continuously photographed in time series, the images are taken from a plurality of observation points, and data on the maximum principal strain rate at the first gauge length and the maximum principal strain rate at the second gauge length are obtained based on images of the fracture portion of the test piece photographed at the plurality of observation points.

5. A method for determining forming limit strain according to any one of claims 1 to 3, wherein the punch on which the test piece is placed in the stretch forming test has a flat placement surface.

6. A method for determining forming limit strain according to any one of claims 1 to 3, wherein the metal is an aluminum alloy.

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