Factors Causing Undesirable Deformations during the Bending of Extruded Sections*

Transcription

1 Materials Transactions, Vol. 47, o. 5 (26) pp to 1359 #26 The Japan Institute of Metals actors Causing Undesirable eformations during the Bending of Extruded ections* huji akaki 1 and oah Utsumi 2 1 epartment of Mechanical Engineering, Tokyo Metropolitan Institute of Technology, Tokyo , Japan 2 epartment of Mechanical Engineering, aculty of Engineering, iroshima Kokusai Gakuin University, iroshima , Japan The authors have investigated the factors causing undesirable deformations of extruded sections subjected to a quasi-uniform bending moment. These deformations include flattening distortion, wrinkling and folding. In this report, the basic mechanism of the flattening distortion of the cross section is explained and effective methods for controlling the undesirable deformation are proposed. The flattening distortion appears as a primary deformation at the beginning of the bending operation and corresponds to the shape of the cross section and the degree of bending. It is clarified that the thickness of the wall, the shape of the cross section and the position of the neutral axis influence the configuration of the flattening distortion. As an example, the bend degree of the wrinkling limit is approximately fourfold when the thickness of the workpiece is doubled. [doi:1.232/matertrans ] (Received ecember 16, 25; Accepted March 2, 26; Published May 15, 26) Keywords: bending, quasi-uniform bending, forming property, extruded sections, flattening, wrinkling limit, aluminum alloy sections 1. Introduction Extruded sections of aluminum alloy have been used as lightweight structure material for automobile frames. Generally, a secondary forming process such as bending is required when the extruded sections are used in this application. Therefore, an effective bending process needs to be developed. In the practical bending process of sections, researchers previously reported undesirable deformation of the cross sections in stretch bending, 1) press bending, 2) the forming property in compression bending 3) and the drawbending process. 4) Basic research has dealt with the influence of material properties on the flattening in pure bending, 5) improvements on the shape distortion in the bending of circular tubes 6) and EM (finite element method) analyses of the bending of sections and pipes. 7) Research on the deformation properties in bending was made on different thicknesses of square tubes; 8) however, there has been insufficient research on the flattening process for extruded sections, such as the deformation at the beginning of bending and the correlation of the shape of a cross section with the degree of bending, and also the wrinkling found in bending. The purpose of this report is to clarify the fundamental characteristics concept of bending, and then to examine methods to improve the working limits of bending and to develop an efficient bending method. Therefore, quasiuniform bending, 9) without any tools and jigs for preventing distortion, was performed in order to correctly understand the deformation properties of bending. irst, the basic mechanism of the flattening distortion of the cross section, along with effective methods for controlling this undesirable deformation, is examined. urthermore, it is clarified that the thickness of the wall, the shape of the cross section and the position of the neutral axis influence the configuration of the flattening distortion. rom this result, we study the *This Paper was Originally Published in Japanese in Journal of JTP 46 (25) working conditions that are effective in preventing the undesirable deformations due to the bending. 2. Experiment 2.1 orkpiece The workpiece materials used in the experiment are aluminum alloys JI A663-O and -T5, and A661-O and -T6. Table 1 shows the mechanical properties of the workpieces. Three types of cross sections are chosen. Type A is a square tube that is hollow. Type B is a square tube containing a reinforcing center rib. Type C is a three-sided, square channel. igure 1 shows the shapes and dimensions. The width and height are 4 mm. The working length L w is 16 mm, or 4 times the height. The workpiece length L is 32 mm, and the wall thickness t is 3., 2., 1.5 or 1. mm. In ig. 1, the symbol indicates the center of the bending radius in each section type. or example, type B1 has a rib which reinforces the two webs; in other words, type B1 has a rib in the circular direction. 2.2 Quasi-uniform bending igure 2 shows a schematic representation of the loading system in quasi-uniform bending. The rotational displacement of the workpiece is constrained around both the x and y axes, thus allowing only translational displacement in the x and y direction and rotational displacement in the x-y plane. The workpiece and the loading arm are connected by Material A663 Table 1 B (MPa) Mechanical properties of material used. (MPa) (%) n C (MPa) T O T A661 O ¼ C" n (Test piece: JI Z A)

2 actors Causing Undesirable eformations during the Bending of Extruded ections 1355 =4 Type : Cross section A : [ ] B1:[ ],B2:[ ] C1:[ ],C2:[ ],C3: [ ] t =4 t Thickness t (mm) 3., 2., 1.5, , 2., 1.5 =4 t δ w=( ) / 2 lattening with wrinkling lattening CL δ C δ C T δ δ =4 =4 =4 ig. 3 Various deformations on the cross section. Type A Type B1 Type C1 ig. 1 hapes and dimensions of the workpiece. ixed end Loading length X= X=4 orkpiece LL=64 Loading arm R d ie Y Load +3% orking length B.M.. L w=4 3% X ig. 2 Loading system and distribution of bending moment. ig. 4 chematic representation of flattening distortion of a square tube. 1) chucking parts of steel plate for moment. 9) The bending moment is applied by the loading arm. The cantilever of the loading length L L is 64 times the height ; thus, the deviation of the bending moment loaded onto the workpiece is 3%. The concentrated load is measured by a load cell attached to the end of the arm. The radius of the bending die R d is 8, 4, 2 or 1 mm, while other R d values of 32, 16, 57, 28 or 14 are assumed by extrapolation. The bend degree =R is the ratio of height to the bend radius R. R d is equal to the bend radius R of the workpiece which is in contact with the bending die. 2.3 eformation of cross-section hen the bending moment is loaded onto the workpiece, the various deformations of the cross section can be seen in ig. 3. The parameters T and C represent the concave distortion of the tension and compression flanges, respectively; represents the convex distortion of the web; CL and C represent each of the uneven wrinkles. 3. Results and iscussion 3.1 Mechanism of flattening distortion igure 4 shows the typical flattening distortion 1) of a square tube. Because the flattening is a fundamental deformation, it is already known that the tension and compression flanges will undergo concave distortions, while the webs will suffer a convex distortion. Through the bending, the flanges of the cross section move in the direction of the neutral axis. Then, the flattening distortion appears as a primary deformation and a decrease of the moment of inertia. The force of the flattening distortion is shown in ig. 5. If we assume that the neutral axis and the center axis of the cross section on the square tube coincide, and the stress-strain curve is given by ¼ C" n, then strain " T and stress T of the outermost layer of the tension flange can be expressed as " T ¼ =ð2þ ð1þ T ¼ Cf =ð2þg n ð2þ where is the radius of the neutral axis, is the height of the square tube, C is the plastic modulus, and n is the workhardening exponent. hen the circumferential forces on point A and B (on the tension flange with an infinitely small angle d) are represented by P T, the flattening component P T can be expressed as 11,12) P T ¼ t Cf =ð2þg n d where P T acts vertically along the distance of A and B (namely, dx T ), t and are constant, and is sufficiently smaller than. As decreases, the flattening force increases and the flattening distortion increases. 3.2 Restraining method of flattening distortion igure 6 shows the flattening distortion of various types of extruded sections. The use of a mandrel inside the extruded ð3þ

3 1356. akaki and. Utsumi (a) Bending stress σ and strain ε Compression side Tension side lattening components ig. 5 Mechanism of flattening components. 11) (P T : Circumferential force of tension side, P C : Circumferential force of compression side, P T : lattening component of tension side, P C : lattening component of compression side) Cross section.a. sections may limit the occurrence of the flattening distortion. or triangle sections, a circular mandrel inscribed in a triangle may be selected. In the case of a square tube, a mandrel controlling only each concave distortion of the tension and compression flanges can be selected. In square tube containing a reinforcing rib in the radial direction, the flattening distortion of type B2 is much smaller than that of type A because of the width of the flange of type B2 is half length of the width of the flange of type A. urthermore, in the channel, type C3, when the concave distortion of the (b).a. lattening ig. 6 Typical shapes of flattening distortion of the cross section. (.A.: eutral axis : Result of EM : Result of experiment) compression flange can be controlled, at the same time, the outer displacement of the webs is disappear. 13) A mandrel should not collapse from the forces of the flattening components, and so it is necessary to select material and shape that can form to the bend radius. or example, the results show that a laminated elastic mandrel is appropriate. The flexural rigidity of this mandrel is approximately 1/1 of that of the workpiece in the elastic state. 4) 3.3 rinkling and splitting ome typical undesirable phenomena in quasi-uniform bending are shown in ig. 7. In ig. 7(a), type A shows wrinkling with concave distortion on the compression flange. The wrinkling is buckling deformation appearing selectively under this working condition. igures 7(b) and (c) show the typical wrinkling of type B1 and B2. In type B1, the rib in the circumferential direction can restrain the convex distortion of the webs but cannot directly restrain the wrinkling of the compression flange. In type B2, the rib in the radial direction can restrain the concave distortion of the tension and compression flanges. The rib is remarkably effective in restraining the wrinkling of the compression flange, because the pitch of the wrinkling is approximately half compared with type A (without the rib in the radial direction). igure 7(d) shows the folding in type C1. Because type C1 does not have a web, the folding appears due to the decrease in the moment of inertia according as the increase in the flattening or wrinkling. igure 7(e) shows the wrinkling in type C2. This specimen does not have the compression flange. Because the neutral axis inclines toward the tension side, the compression region of the web increases. Thus, wrinkling occurs easily in type C2, when the webs are not restrained to move out of its plane. In ig. 7(f), type C3 shows splitting on the tension side of the webs. 3.4 eformation mode hen the extruded sections are subjected to the moment in quasi-uniform bending, undesirable phenomena consist of (a) flattening distortion, (b) wrinkling, (c) folding, (d) necking, and (e) splitting. igure 8 shows the undesirable phenomena appearing on the cross sections of the extruded sections; the phenomena in this table are labeled for flattening distortion, for wrinkling, for folding, for necking, and for splitting. or the bend degree =R ¼ :13{:1 (type A, A663- O, t ¼ 3:), only the flattening distortion appears on the cross section, as shown in ig. 8(a). or the bend degree =R ¼ :14, wrinkling deformation appears on the compression flange, and for the bend degree =R ¼ :4, wrinkling deformation appears on the web of the compression side. As the workpiece of the thin thickness is bent, wrinkling deformation easily appears on the compression flange. Thus, the bend degree of the wrinkling limit is approximately fourfold when the thickness of the workpiece is doubled. On the other hand, the bend degree of the wrinkling limit of A663-O is higher than that of A663- T5. According to another result, 9) the bend degrees of the wrinkling limit and deformation mode of A661 are similar to those of A663. The result of type A compares with the results of type B1

4 actors Causing Undesirable eformations during the Bending of Extruded ections 1357 (a) (b) (c) Type A, rinkling, A663-O,t =1.5, /R= (d) Type B1, rinkling, A663-O,t =1.5, /R= (e) Type B2, rinkling, A663-O,t =1.5, /R= Type C1, olding, A661-T6,t =2., /R= (f) Type C2, rinkling, A661-T6,t =1.5, /R= Type C3, plitting, A661-T6,t =3., /R=.29 ig. 7 Typical undesirable phenomena under quasi-uniform bending moment. and type B2, as shown in ig. 8(b). The bend degree of the wrinkling limit in type A is =R ¼ :25, and in type B2 it is =R ¼ :1. Compared to the bend degree of the wrinkling limit in type A, type B2 is fourfold because the reinforcing rib in the radial direction efficiently controls the flattening distortion and the wrinkling of the compression flange. In type B1, it is possible to control the concave distortion because the reinforcing rib restrains the webs. owever, it does not directly control the flattening distortion. Therefore, type B2 effectively controls the flattening distortion and the wrinkling in the bending of the square tube. The results of type C in three-directional quasi-uniform bending are shown in ig. 8(c). In type C, as in type A and type B, as the bend degree =R increases, wrinkling appears on the compression flange first, then on the web. In type C2, there is no compression flange and the bend degree of the wrinkling limit is low. Because type C2 has no compression flange, the neutral axis exists near the side of the tension flange. Thus, the compression strain at the free edge of the web increases. urthermore, wrinkling can easily appear on the web because it is impossible to restrain the out-of-plane displacement on the web. In the bending of extruded sections, each structural member of the cross section undergoes the flattening distortion and wrinkling respectively, according to its own position; in other words, the effects extend to other structural members. owever, the folding on the whole cross section arises under decreasing of the moment of inertia by the flattening distortion or the wrinkling. 3.5 Relationship between wrinkling and bending moment igure 9 shows the relationship between the bend degree =R and the deformation of the cross section for the bending moment using type A (t ¼ 2:, A661-O). As the bend degree =R increases, the convex distortion of the tension and compression flanges becomes a linear and stable deformation. rinkling appears from approximately the bend degree =R ¼ :7. It is easy to distinguish CL and C (the uneven wrinkles with flattening distortion, as shown in ig. 3). The wrinkling that appears with the increase in the bend degree =R is buckling deformation. Because the concave distortion of tension T is defined by the position of the neutral axis, the influence of the wrinkling of the

5 1358. akaki and. Utsumi (a) A O A T 5 Bend degree / R Bend radius R (mm) R :4.14 R :2.29 R :14.4 R :1 R :4.14 R :2 Thickness t (mm) (b) A O Bend degree / R Bend radius R (mm) R :4.14 R :2 eformation of the flanges and webs : lattening distortion : olding : rinkling : plitting : ecking Tension flange Thickness t =1.5(mm) Type A Type B1 Type B2 [ ] [ ] [ ] eb eb Type B Compression flange (c) Cross section Type C1 [ ] Type C2 [ ] Type C3 [ ] Bend degree / R Bend radius R (mm) R :4.14 R :2.29 R :14 Thickness t (mm) Type C( A661-T6 ) 3. Type A ig. 8 eformation mode of various extruded sections under quasi-uniform bending moment. δ CL, δ C, δ T.15.5 δ T δ CL, δ C : :eformation of tension flange eformation of compression flange Buckling limit Bend degree / R M/t δ CL δ T δ C compression flange is negligible. In regard to the bending moment, the buckling limit does not agree with the maximum bending moment because the influence of work-hardening in bending precedes that of the wrinkling in the compression flange Bending moment M/ t (k m m ) ig. 9 Buckling behavior of the cross section and the bending moment. (A661-O, Type A, t ¼ 2: mm, ¼ ¼ 4 mm) 4. Conclusions (1) Undesirable deformations in the bending process of extruded sections consist of (a) flattening distortion, (b) wrinkling, (c) folding, (d) necking and (e) splitting. The flattening distortion as primary deformation appears through the bending operation. The wrinkling and the folding appear as buckling deformation with an increase in the bend degree =R. The necking and the splitting depend on the ductility of the material. (2) On the flattening distortion, each element of the cross section of the extruded section moves in the direction of the neutral axis because of the flattening component. The flattening forces increase as the area becomes distant from the neutral axis. (3) Though the form of flattening distortion differs depending on the shape of the cross section of the extruded section, the mechanism for the deformation is the same. hen the forms of the flattening distortions are clarified by EM simulation, it is possible to estimate the optimal shape of the mandrel and the effects of the working conditions. (4) The wrinkling never appears at the beginning of the bending operation because the progress in bending causes the buckling (wrinkling). In hollow square tube, the bend degree of the wrinkling limit is approximately fourfold when the thickness of the workpiece is doubled.

6 actors Causing Undesirable eformations during the Bending of Extruded ections 1359 (5) In square tube containing a reinforcing rib in the radial direction, the reinforcing rib prevents the flattening distortion and wrinkling. The bend degree of working limit in this type is approximately fourfold compared to that in hollow square tube. (6) In channel type sections, the three-directional bending differs according to the position of the neutral axis. In channel without a compression flange, the bend degree of the wrinkling limit is low. In this type, the neutral axis exists near the side of the tension flange. Thus, the compression strain of the web increases. urthermore, wrinkling can easily appear on the webs, when the working condition of the out-of-plane displacement on the web is free. The bend degree of the wrinkling limit in channel without tension flange is approximately fourfold compared to types the other two types of channel section. Acknowledgments The authors would like to express their thanks to the Committee of orming Research of the Extruded ections at the Japan Institute of Light Metals for providing the extruded sections, and also to the AMAA oundation for Metal ork Technology for their financial aid. REERECE 1) M. Ueda, K. Ueno and M. Kobayashi: Journal of JTP 25 (1984) ) O. asegawa and. isimura: J. JILM 46 (1996) ) The Committee of orming Research of the Extruded ections: The Report of Branch Research Committees, o. 36 (JILM, 1999) ). Utsumi and. akaki: J. Materals Processing Technology 123 (22) ) J. Endo and T. Murota: Journal of JTP 23 (1982) ) J. Endo and T. Murota: Journal of JTP 27 (1986) ) Y. Yokouchi and Y. Mune: Proc Japanese pring Conference for the Technology of Plasticity, (JTP, 1995) ). J. uchs, Jr.: Bell. yst. Tech. J. 38 (1959) ) The Committee of orming Research of the Extruded ections: The Report of Branch Research Committees, o. 32 (JILM, 1996) ). akaki, T. Toin and T. arasima: Journal of JTP 36 (1995) ). akaki: Proc. Tokyo Metropolitan Institute of Technology 15 (Tokyo Metropolitan Institute of Technology, 21) ). akaki and. Utsumi: Proc. 7th Inter. Conf. on Advanced Technology of Plasticity, ed. by M. Kiuch,. ishimura, J. Yanagimoto, (Japan ociety for Technology of Plasticity, 22) Vol. 2, ). akaki,. Utsumi, K. Taguchi and O. asegawa: J. JILM 49 (1999)