Mechanics of Materials
Influence of 1st Step Shape on Formability of Circular Truncated Cone Stretch Forming in Two-Step Forming
2022 年 63 巻 3 号 p. 311-318
詳細
2022 年 63 巻 3 号 p. 311-318
The formability of steel sheets must be improved in order to form complicated car parts. Multistep forming is one way to improve formability. Although the shape after preforming can influence formability in the main step of multistep forming, no relationship has been reported between the shape after preforming and the final shape in stretch forming.
In this study, circular truncated cones were formed by a two-step forming process consisting of preforming and main forming with combinations of various shapes after preforming and final shapes in order to investigate the effect of the shape after preforming on the forming limit in main forming. The results confirmed that the forming limit height in main forming is affected by the preforming shape. It was also found that the forming limit height in main forming is determined by the central cross-sectional line length of the shape after preforming.
This Paper was Originally Published in Japanese in J. JSTP 61 (2020) 87–92. Abstract was slightly modified.
Fig. 13 Relationship between central cross-sectional line length after preforming and main forming (DM ≧ DP).
Needs for application of ultra-high strength steel sheets to automobile frame parts and high designability in automotive outer panel parts have increased in recent years. Therefore, the development of a technology which improves these press formability of the steel sheets is required.
The typical forming defects which are problems in press forming are cracks, wrinkles, shape defects, and surface distortion, and among these defects, cracks are the most serious type.1) Cracks are further classified into drawing cracks, stretch cracks, stretch flange cracks, bending cracks, etc. according to the forming method.2) In particular, it is important to prevent drawing cracks and stretch cracks, which often occur in the product shape. As approaches for preventing these type of cracks, research and development are carried out from the viewpoints of materials and forming technology. From the material viewpoint, the effects of the mechanical properties of materials on formability in each forming mode have been clarified, and the effects of these property values on press formability have been arranged, reported, and used in material development.1)
As one forming technique for improving formability, multistep press processes have been applied to prevent cracks by increasing the number of press processes. In multistep forming, it is important to optimize the shape in each step. The reported shape design method for each process in multistep deep drawing include the formability improvement effect of reverse bulging,3) the initial blank shape design method by a slip line field in square punch drawing,4) improvement of the forming limit by reverse drawing in cylindrical deep drawing,5) etc. However, application of these methods is very limited and there have been no reports on the effect of the shape in each step on the final formability, or the effect of the design method of the optimum shape in each step on stretch forming by multistep processes. Stretch forming is different from deep drawing, in which material is supplied from the flange, because stretch forming is carried out using only the material in the die without material supply from the flange. Since the movement of the material is restricted by the frictional force in the region where the material and the die are in contact during press forming, strain is concentrated locally, resulting in crack generation. In order to avoid such cracks, it is necessary to disperse this strain,6) and in order to disperse strain in multistep processes, it is important to optimize the shape in each step.
In this report, a FEM analysis and experiment were carried out on forming using a combination of punches with different shapes in each step in two-step truncated cone stretch forming, and the effect of the shape in the first step (hereinafter, preforming) on the formability in the second step (hereinafter, main forming) was investigated.
In order to investigate the influence of the preforming shape on formability in main forming, a FEM analysis was performed for truncated cone stretch forming with different punch diameters and punch shoulder radii in each step. Experiments were also carried out to verify the accuracy of the analysis under some conditions.
The analysis was carried out by the dynamic explicit method using LSDYNA Ver 9.7.1R5. All the dies were constituted by rigid shell elements. The die diameter was 153 mm, the die shoulder radius was 5 mm, and the blank holder diameter was 153 mm, and the punch diameter and punch shoulder radius were changed in preforming and main forming. The punch diameter and punch radius in the preforming process are denoted DP, and RP, respectively, and in main forming, the punch diameter and shoulder radius are denoted DM and RM. The tested DP and RP combinations and the preforming limit height are summarized in Table 1. DM was set to 3 levels of 50 mm, 100 mm, or 150 mm, RM was set to 5 mm, and the blank shape was a circle with a diameter of 170 mm. A multi-linear approximate isotropic elastic-plastic model was used as the material model in this analysis. The stress-strain curves and n-values were obtained from the experiment. The stretch forming test was simulated using a blank mesh size of 1.0 mm and a friction coefficient with the die of 0.15, and the circumference was restrained in the radial direction. The die configuration is shown in Fig. 1. The material used in the analysis and experiments was JAC 270 D with the mechanical properties shown in Table 2. Fracture was judged from the principal strain distribution after the analysis and the Keeler-Goodwin diagram.7,8) The forming limit was defined as 99% of the breaking height in both preforming and main forming, and main forming was carried out using the formed article obtained at the forming limit of the preformed sample. The preformed height is shown in Table 1. The items obtained in the analysis were the forming limit height, the center cross-sectional shape at the forming limit, the center cross-sectional line length, and the thickness reduction rate of the punch bottom. The thickness reduction rate of the punch bottom was obtained for the area from 5 mm from the center to the outside of the punch bottom in order to avoid a region in the center of the punch bottom which a radius about 5 mm, where the thickness reduction is peculiarly small.
Tool models for FEM.
An experiment to verify the accuracy of the analysis was also conducted using the material shown in Table 2. The preforming conditions were the 3 patterns of DP = 100 mm and RP = 5 mm, 10 mm, or 20 mm, and the main forming conditions were also the 3 patterns of DM = 50 mm, 100 mm, or 150 mm, and RM = 5 mm, for a total of 9 test patterns. First, a preformed die was used for the test. The height when constriction was confirmed visually was defined as the breaking height, and samples of with 99% of that height were used as preformed samples. The preformed heights are given in Table 1. The experimental results showed that the preforming height was lower than the analytical result. This difference is considered to be caused by differences in the lubrication condition and, constraint condition, and the fact that the cracks were judged visually. In main forming, the product was formed to the height at which constriction was confirmed visually, and 99% of that height was defined as the forming limit height. The test was conducted with material inflow restrained by a lock bead with a diameter of 170 mm in both preforming and main forming, and the lubrication condition was the rust prevention oil that adhered to the steel sheet from the start of the test.
The accuracy of the analysis was verified by comparing the results of the experiment and the analysis. The experiment was conducted with the total of nine patterns described in Chapter 2. The analysis was carried out with the same combinations of punch conditions as in the experiment, and the forming height was compared. The results are shown in Fig. 2. From Fig. 2, the forming limit height increased with the expansion of RP under all the experimental and analytical conditions, showing the same tendency in the experiment and analysis. Cracks initiated from the punch shoulder under all experimental and analytical conditions Based on these results, it is considered that the tendency of the actual test can be simulated by the analysis. Therefore, the following examination will be carried out using the analytical results. The analytical results are classified into three types according to the relationship between DP and DM, as discussed in the following sections, and show the relationship between the breaking limit height and the preformed shape.
Dependence of forming limit height in main forming on punch shoulder radius.
As an example, Fig. 3 shows the forming limit height when DP and RP are DM = 50 mm and RM = 5 mm. Here, the blank plot is the result of forming with a punch diameter of 50 mm and a punch shoulder radius of 5 mm in one step without preforming (hereinafter, this one-step process is called single forming). In comparison with single forming, the forming limit height was improved by preforming under all conditions. Although the forming limit height increases with increases in RP, no effect of DP recognized. Figure 4 shows the thickness reduction rate of the punch bottom after main forming. The thickness reduction rate in preforming was equal to or less than that in single forming except under the condition that RP 20 mm. In addition, body wrinkles, as shown in Fig. 5, occurred during main forming under all conditions of DM < DP. This defect occurs because the material which was stretched in the circumferential direction in the vicinity of the punch shoulder in preforming buckled in main forming. Thus, the condition of DM < DP is not suitable for preforming in practical use because it is difficult to press the material which is once stretched without causing buckling in the vertical wall and oblique wall.
Dependence of forming limit height on punch shoulder radius of preforming (DM < DP).
Effect of punch shoulder radius of preforming on thickness reduction at punch top in final shape (DM < DP).
Wrinkles in main forming (DM < DP).
As an example, Fig. 6 shows the forming limit height at each punch diameter when RM = 5 mm and RP is changed. Here, the blank plot is the result of single forming. The forming limit height was improved with expansion of RP under all DP conditions. Figure 7 shows the thickness reduction rate of the punch bottom. When DM = DP, the decrease rate of the punch bottom thickness after main forming was larger than the decrease rate of the thickness in single forming under all preformed DP and RP conditions.
Dependence of forming limit height on punch shoulder radius of preforming (DM = DP).
Effect of punch shoulder radius of preforming on thickness reduction at punch top in final shape (DM = DP).
As an example, here, DM = 150 mm and RM = 5 mm, and the forming limit height when DP and RP are changed is shown in Fig. 8. The blank plot is the result of single forming. The forming limit height in this forming was improved under all the preformed conditions. At the same DP, the forming limit height was higher for larger RP, and at the same RP, the forming height was higher for DP = 100 mm than for DP = 50 mm. Figure 9 shows the thickness reduction rate of the punch bottom after main forming. Under the condition of DM > DP, as in the case of DM = DP, the thickness reduction rate of the punch bottom was larger than that in single forming under all conditions. When preforming was carried out, the forming limit height of this forming was highest under the condition of DP = 100 mm, and the thickness reduction of the punch bottom was highest under the condition of DP = 50 mm. When DM > DP, the bending mark of the punch shoulder during preforming remained at the punch bottom after main forming (Fig. 10) because die side forming and pressurization at the bottom dead point were applied in order to obtain the forming limit height in this examination. However, it seems to be possible to avoid this problem by relaxing pressurization at the bottom dead point.
Dependence of forming limit height on punch shoulder radius of preforming (DM > DP).
Effect of punch shoulder radius of preforming on thickness reduction at punch top in final shape (DM > DP).
Bend mark in final shape caused by punch shoulder in preforming.
Figure 11 shows the relationship between the forming height in the preform and the forming limit height in main forming when using a constant DM = 150 mm and various values of DP and RP. At each DP, the forming height in both preforming and main forming increases as RP is increased. However, the forming limit height of main forming cannot be uniformly adjusted by the forming limit heights of RP and DP and preforming because it is stratified by DP.
Relationship between forming limit height in main forming and preforming.
In Chapter 3, it was shown that the forming limit height in truncated cone forming was improved by preforming, and the amount of improvement varied depending on the combination of the punch shape in preforming and that in main forming. In this chapter, we consider what factors affect the forming limit height.
4.1 Relationship between cross-sectional line length of preform and cross-sectional line length of main formingThe length of the center cross section shown in Fig. 12 was defined as a parameter representing the formability in preforming and main forming.
Definition of central cross section.
Figure 13 shows the relationship between the center cross-sectional line length after preforming and the central cross-sectional line length after main forming under the condition of DM ≧ DP. Here, the blank plot shows the result of single forming. It can be seen that the cross-sectional line length after preforming is almost equal to the central cross-sectional line length after main forming. This result shows that, under the condition of DM ≧ DP, the deformation in which the central cross-sectional line length increases from the preform to the main form is small.
Relationship between central cross-sectional line length after preforming and main forming (DM ≧ DP).
Figure 14 shows the central cross sectional shape and the thickness reduction rate in both steps when main forming was performed under the conditions of (DM, RM) = (150 mm, 5 mm) after preforming was performed under the conditions of (DP, RP) = (100 mm, 20 mm) (Fig. 14(a)) and (DP, RP) = (50 mm, 20 mm) (Fig. 14(b)). The horizontal axis is the projected distance x in the press direction from the center of the punch bottom.
Central cross-sectional shapes and distributions of thickness reduction after preforming and main forming.
Under either condition, thickness reduction of the part which was the punch bottom in preforming does not proceed in main forming, and thickness reduction proceeds only in the part which was the vertical wall in preforming.
Figure 15 shows the thickness reduction rates of the punch bottom after preforming and after main forming under the condition of DM ≧ DP. The blank point is the result of single forming. Regardless of DP and RP, the thickness of the punch bottom did not decrease in main forming.
Relationship between thickness reduction at punch top after preforming and after main forming.
Figure 16 shows the amount of material movement in the radial direction from the start of forming to just before breaking when DM = 150 mm and RM = 5 mm is formed in single forming (Fig. 16(a)) and when DM = 150 mm and RM = 5 mm is formed after preforming at DP = 100 mm and RP = 20 mm (Fig. 16(b)). Figure 17 shows the vector display of the direction and magnitude of the maximum principal strain just before rupture near the radius part of the punch shoulder in single forming (Fig. 17(a)) similar to the conditions in Fig. 16, and in main forming after preforming (Fig. 17(b)). From Fig. 16, it can be seen that the material moves more in the radial direction when preforming is applied, and from Fig. 17, the radial direction is the maximum principal strain direction when single forming was done, whereas the circumferential direction is the maximum principal strain direction when preforming was done. From these results, it is considered that large tension is not generated when preforming is carried out because the preformed material is moved from the punch bottom to the radial direction during forming, while tension is generated because the material is insufficient in the circumferential direction. Subsequently, as shown in Fig. 15, the thickness reduction rate of the punch bottom is the same in the preform and the main forming, so when there is no material that can move from the punch bottom, the material of the punch bottom does not elongate further and breaks. As a result, in main forming, the material is extended in the circumferential direction, but the extension in the radial direction is small, and it is considered that thickness reduction proceeds without changing the central cross-sectional line length in preforming and main forming.
Material displacement until just before fracture.
First principal strain distributions and their directions just before fracture.
In order to maximize the forming height in main forming, it is considered effective to maximize the cross-sectional line length of the preform, because the cross-sectional line lengths of the preform and the main forming are almost equal, and as the cross-sectional line length in main forming increase, the forming height geometrically becomes higher.
4.3 Conditions for maximizing cross-sectional line length of preformAs shown in Fig. 14, the forming limit height in main forming increase as the cross-sectional line length of the preform become longer. Figure 18 shows the relationship between DP and the cross-sectional line length of the preform for each RP. As shown in Fig. 18, the cross-sectional line length of the preform has an extreme value. Under these test conditions, the cross-sectional line length of the preform has a maximum at DP = 100 mm and RP = 20 mm.
Dependence of central cross sectional line length after preforming on punch radius after preforming.
The reason why the cross-sectional line length of the preform has an extreme value is considered in the following.
Figure 19 shows the relationship between the punch diameter of the preform and the decrease rate of the punch bottom thickness. When the punch shoulder radius is the same, the punch bottom thickness reduction rate of the preform decrease as the punch diameter increase, and when the punch diameter is the same, the punch bottom thickness reduction rate decreases as the punch shoulder radius decreases. Figure 20 shows the cross-sectional shape and maximum principal stress distribution at the forming limit height of the preform for DP = 100 mm, 150 mm and RP = 5 mm. The maximum principal stresses near the punch shoulder on the vertical wall side, which are the fracture initiation sites, are almost equal regardless of the punch diameter because they are in the state just before the fracture. However, as the punch diameter increases, the maximum principal stress at the punch bottom decreases. As shown schematically in Fig. 21, the angle of the vertical wall becomes steeper as the punch diameter increases. As the length of the blank in contact with the punch shoulder radius increases and the angle becomes steeper, the force component pressing the material against the punch shoulder becomes greater and the friction force becomes higher. It is also thought that the material transfer from the punch bottom to the vertical wall was inhibited by the increase in the bending resistance in the punch shoulder part9) as the punch shoulder radius decreased, and as a result, the forming height was reduced and the stress and strain of the punch bottom decreased.
Dependence of thickness reduction after preforming on punch diameter after preforming.
Central cross-sectional shapes and distributions of first principal stress after preforming.
Pattern diagrams of punch shoulder cross section.
Since the elongation of the material of the punch bottom is expressed by the product of the punch diameter and the strain of the punch bottom and the strain of the punch bottom decreases as the punch diameter increases, the elongation of the punch bottom in the preform has an extreme value for the punch diameter. As a result, as shown in Fig. 18, it is considered that the cross-sectional line length also had an extreme value for the punch diameter. Thus, there is an optimum punch diameter for maximizing the elongation of the punch bottom. Preforming at the optimum punch diameter maximizes the cross-sectional line length, and as a result, it is considered that the forming limit height in main forming can be maximized.
As an example, Fig. 22 shows the cross-sectional shapes of preforming and main forming when (DP, RP) = (150 mm, 20 mm) (Fig. 22(a)) and (DP, RP) = (100 mm, 20 mm) (Fig. 22(b)) were preformed before main forming with (DM, RM) = (150 mm, 5 mm) and as a comparison, when single forming with (DM, RM) = (150 mm, 5 mm) was performed. As shown in Fig. 22(a), when only the punch radius of the preform and the main form is changed, the forming height is improved by 55% compared with single forming. However, by optimizing the punch diameter of the preform as shown in Fig. 22(b), the forming height can be improved by about 80% compared with single forming.
Central cross-sectional shapes after preforming and main forming ((DM, RM) = (150 mm, 5 mm)).
According to the concept of ordinary die design, a process using a forming punch radius in the restrike process of DM = DP, RM < RP is frequently applied, as shown in Fig. 22(a). However, preforming with a DP of the optimum diameter, as shown in Fig. 22(b), maximizes the cross-sectional line length in the preform, and as a result, the forming height in main forming can be maximized.
Formability in truncated cone overhang forming by a 2 step process was investigated using punches in with different diameters and shoulder radii in each step. The following conclusions were obtained.
