2019 年 60 巻 4 号 p. 538-543
The purpose of this research is the development of technology to make complex-shape closed-section parts directly from sheet blanks (direct sheet forming). It is expected to form closed-section parts with large expansion of the circumferential length by direct sheet forming. In this paper, the deformation type of horn tubes, which consists of circular, conical and transient portions, is studied. The horn tube is one of the typical shapes for automotive parts. With reference to deformation types in the conventional stamping process, those in the forming process of horn tubes are discussed on the basis of the results of FEM analysis. The validity of FEM analysis is confirmed by comparison with experimental results. It is clarified that the forming process can be broken down into several stages and deformation types (uniform bending of sheet, stretch flanging, axial bending of U-section, deformation into double curved surface and plane-strain compression).
This Paper was Originally Published in Japanese in J. JSTP 59 (2018) 27–31.
The automobile industry demands lighter car bodies and higher strength in order to meet stricter environmental controls on exhaust emissions and legal regulations on collision safety improvement.1) To contribute to meeting these demands, the application of closed section members to car bodies is advancing. Closed section parts provide increased body rigidity and improve the strength/weight ratio.
Most conventional closed section parts are fabricated from tubular blanks such as electric welded steel pipes. For instance, tube hydroforming2,3) is widely implemented in the fabrication of closed section parts; however, it is difficult to form a part that significantly varies in sectional circumferential length because an electric welded steel pipe has a uniform cross section in the longitudinal direction. Several studies have reported that the circumferential length could be transformed significantly using movable dies,4) however, the die has a complicated structure. While there are also reports5,6) in which sheet blanks could be fabricated into 3D-shaped closed section parts, there are so few fundamental research reports with systematically organizing. Baba et al.7) transformed sheets into a closed section by UO bending, however, they dealt with 2D bending deformation of sheets.
The aim in this research is to establish a technology (direct sheet forming) that allows the formation of complicated 3D-shaped closed section parts directly from sheets. The direct sheet forming of horn tubes, which consists of circular, conical and transient portions, is discussed in this paper. The horn tube is one of the typical shapes for automotive parts. With reference to deformation types8) in conventional stamping process, deformation types in the forming process of horn tubes are discussed on the basis of the results of FEM analysis. Clarification of deformation types is important for universal understanding and formability evaluation of horn tubes with various dimensions and materials. The validity of FEM analysis is confirmed by comparison with experimental results.
Mechanical properties and thickness of cold rolled steel sheets used in forming experiments are shown in Table 1. Dimensions of the horn tube are shown in Fig. 1. The circular portion with outer diameter of 40 mm and the conical portion with taper angle of 6.7° are smoothly connected via the transient portion with constant curve-radius of 250 mm. The full length is 300 mm and the transient portion is situated in the middle of the longitudinal direction. Each portion encircled with a dotted line in the cross-section view in Fig. 2 is referred to as the edge portion, bottom portion, side wall, and side portion, respectively. In addition, LL, LH, LW, and θC are defined as, respectively, the length in the longitudinal direction with origin at the end of tubes on the side of the circular portion, the length in the height direction with origin at the position of the neutral plane calculated from the sectional shape, the length in the width direction with origin at the middle of the side portion, and the angle in the circumferential direction with origin at the middle of the bottom portion.
Dimensions of the horn tube.
Forming processes using sheet blank.
A blank sheet is shaped up by smoothly connecting between developed shapes into plane of the conical portion and the circular portion. As shown in Fig. 2, horn tubes are formed from blank sheets through two processes of U-shaping and closing. Dimensions of lower dies in both processes are shown in Fig. 3. Lower dies in U-shaping and closing processes have same dimensions in the top view, and the clearance between the lower die and the punch is 2 mm (same as the thickness of the blank sheet). Anti-rust oil coated when steel sheets are shipped is used as lubricant. Neither additional lubricants nor degreasing are provided. Grid-shaped lines (2.6–6.2 mm in the longitudinal direction, and 6.0–6.6 mm in the circumference direction) are drawn in advance with laser beams on the surface of blanks. Strain distributions induced in forming processes are calculated by measuring the grid dimensions before and after forming as well as during the process of forming.
Dimensions of lower dies.
Appearances of formed products are shown in Fig. 4. Horn tubes are formed into favorable shapes without gaps in edge portions, breakages nor wrinkles.
Appearance of the trial product.
Forming analysis of horn tubes is conducted using FEM. While forming is carried out through two processes, each process can be broken down into several stages by the detailed observation focusing on stretch and shrink in the longitudinal direction. Deformation in the longitudinal direction is a feature in the forming of 3D shapes. Deformation types in the forming horn tubes are clarified by comparing strain distributions to models which have shapes considered to be typical in each deformation type (simplified models). Strain values employed in the study of the deformation type in each stage are increments from the previous stage (Fig. 5, Fig. 6, Fig. 7 and Fig. 8).
Longitudinal strain distribution induced in each stage (calculated values at the center of thickness).
Longitudinal strain distributions at the edge of the horn tube (2nd stage) and the simplified model for stretch flanging.
Longitudinal strain distributions at the middle cross section of the horn tube (3rd stage) and the simplified model for axial bending of U-section.
Longitudinal strain distribution at the upper side of middle cross section of the horn tube (4th stage).
PAM-STAMP which is the universal code of the dynamic explicit method is used for FEM. Tools are assumed as rigid bodies. Blank sheets are modeled using shell elements, and the material properties are approximated by the Swift formula from stress-strain diagrams obtained in tensile tests. Meshes are initially divided into 75 elements (approximately 4 mm) in the longitudinal direction and 26 elements (approximately 4.6 mm) in the circumferential direction. The refinement function that enables the elements in largely deformed portions to be automatically re-divided (into four equal parts) is employed. Five integral points are used in the thickness direction. Note that contour diagrams appear to have gaps at edge portions after forming, nevertheless, no such gaps remain actually. The cause of gaps in contour diagrams is that each element has a distance for determining contact with other elements even at edge portions.
3.2 Study resultsAs shown in Table 2, two processes can be broken down into five stages as the deformation progresses.
The 1st stage is the very early term of the U-shaping process. The sheet contacts with the punch only at both ends of the tube. The sheet has no curvature in the longitudinal direction at the bottom portion. Moreover, the side wall has no curvature in the longitudinal direction either since the gap between the punch and the lower die is wide. It is confirmed by FEM analysis that circumferential strain in bending is induced, however, little strain is induced either in the longitudinal or circumferential direction on the neutral plane. Consequently, deformation type in the 1st stage of forming horn tubes is the bending of sheet.
The 2nd stage is the term until the bottom portion of the sheet comes into contact with the transient portion of the lower die. As in the 1st stage, the bottom portion of the sheet contacts with the punch only at both ends of the tube, and has no curvature in the longitudinal direction. Meanwhile, the gap between the punch and the lower die becomes narrower, the side wall becomes pinched between the punch and the lower die. The side wall of the sheet rises while holding the curvature in the longitudinal direction. The distribution of the strain induced in the 2nd stage is shown in Fig. 5(a) and Fig. 6. The longitudinal strain is small at the bottom portion, and increases linearly from the bottom portion toward the edge portion. Viewing the variations of the longitudinal strain along the longitudinal direction at the edge portion (Fig. 6), the strain shows the maximum value in the vicinity of the center of transient portion and gradually decreases in circular and conical portions. Little longitudinal strain is induced near both ends of the tube. Such features of the strain distribution suggest that the deformation type in the 2nd stage is the stretch flanging. The strain distribution induced in the 2nd stage is compared to that of the simplified model (Fig. 6). The simplified model is the flange up processing of the shape that with the curvature in the longitudinal direction in the top view (same as the transient portion of horn tube), but without curvature in the side view (different from the horn tube). Strain distributions of the horn tube and the simplified model are in good agreement, so that, it is confirmed that the deformation type in the 2nd stage of forming horn tubes is the stretch flanging.
The 3rd stage is the end term in the U-shaping process. The bottom portion of the sheet is pinched between the punch and the lower die with the curvature in the longitudinal direction. The distribution of the strain induced in the 3rd stage is shown in Fig. 5(b) and Fig. 7. Compression strain in the longitudinal direction is induced at the bottom portion, differently from that in the 2nd stage (Fig. 5(a)). The longitudinal strain changes from compression at the bottom portion to stretch at the edge portion (Fig. 7), at the middle cross section (transient portion). The longitudinal strain has an approximately linear relationship to the length in the height direction of the cross section LH. Accordingly, the deformation type in the 3rd stage is expected as the axial bending of U-section. A comparison with the simplified model is shown in Fig. 7. The simplified model is the axial bending of the shape that with the curvature in the longitudinal direction in the side view (same as the transient portion of horn tube), and with the uniform U-shape cross section (different from the horn tubes). Strain distributions of the horn tube and the simplified model are in good agreement, so that, it is confirmed that the deformation type in the 3rd stage of forming horn tubes is the axial bending of U-section.
The 4th stage is until just before the stroke end in the closing process. Edge portions (right and left) advance along the upper die, and contact each other. Side walls of the sheet, retaining the curvature in the longitudinal direction, fall down to the horizontal direction. The 4th stage is forming of the composite shape with curvatures in two directions shown in Table 2. The distribution of the strain induced in the 4th stage is shown in Fig. 5(c) and Fig. 8. Only values at the upper half of the horn tube are shown in Fig. 8, since the lower half has been formed by the 3rd stage and does not deform in the 4th stage. The abscissa denotes length in the width direction LW. No strain is induced at the 90° position of the side portion in either the measured values or the calculated values. The strain increases linearly toward the edge portion as in the stretch flanging.
The 5th stage is near the stroke end in the closing process. The sheet contacts closely with upper and lower dies, and the circumferential length of the sheet slightly decreases. The curvature in the circumferential direction is induced at the edge portion.9) Circumferential strain distributions in the closing process are shown in Fig. 9. The strain in Fig. 9 is value including the amount induced in the U-shaping process. The compressive strain at the transient portion induced before the stroke end (Fig. 9(a)) is due to the stretch flanging and axial bending in the 2nd, 3rd and 4th stages. Thereafter, since the compressive stress in the circumferential direction increases just before the stroke end, the compressive strain in the circumferential direction is induced over the entire of the longitudinal direction (Fig. 9(b)). Note that the sheet contacts closely with dies and the friction between the sheet and dies is large in this stage. The longitudinal strain is hardly induced except around the ends of the tube. The strain state diagram at the cross section between circular and transient portions (large compression strain in the circumferential direction is induced at the section) in the closing process is shown in Fig. 10. The longitudinal strain hardly increases while the circumferential strain increases just before the stroke end (2 mm). The deformation type in the 5th stage is the plane-strain compression.
Circumferential strain distribution after 2nd process (calculated values at the center of thickness).
Strain diagram on the boundary cross section between the circular and transient portions in the closing process.
Horn tubes are formed through the five stages. Strain distributions after each stage are shown in Fig. 11 and Fig. 12. Figure 11 shows distributions at edge and bottom portions. Figure 12 shows distributions at the middle cross section. Strains are measured values including the amount induced in preceding stages. The stretch strain in the longitudinal direction induced at the edge portion increases stepwise in each stage from the 2nd stage to the 4th stage. The compression strain in the longitudinal direction at the bottom portion is induced mainly in the 3rd stage and does not increase in the 4th stage.
Strain distributions at the edge and the bottom (measured values).
Strain distributions at the middle cross section (measured values).
Comparison of the longitudinal strain at the edge portion after the 4th stage is shown in Fig. 13. Calculated values are in good agreement with measured values for the accumulated values of strain induced in each stage.
Measured and calculated strain distributions at the edge after 4th stage.
A fundamental study was carried out using experiments and FEAs on the technology to form three-dimensional closed-section parts directly from sheet (direct sheet forming). The deformation type of a horn tube, which consists of circular, conical and transient portions, was studied. The horn tube is one of the typical shapes for automotive parts.
While the horn tube was formed through two processes, each process can be broken down into five stages. The 1st stage is the very early term of the first process, and is the bending of sheet. The 2nd stage is the term until the bottom portion of the sheet comes into contact with the transient portion of the lower die, and is the stretch flanging. The 3rd stage is the end term in the first process, and is the axial bending of U-section. The 4th stage is until just before the stroke end in the second process, and is the forming of the composite shape with curvatures in two directions. The 5th stage is near the stroke end in the second process, and is the plane-strain compression.
Studies on deformation type could be applied to shapes other than horn tubes. Understanding of deformation types is important to make clear the deformation behavior of complex shapes.
