Deformation and Energy Absorption of Aluminum Square Tubes with Dynamic Axial Compressive Load* 1

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1 Materials Transactions, Vol. 44, No. 8 (23) pp to 157 #23 The Japan Institute of Light Metals Deformation and Energy Absorption of Aluminum Square Tubes with Dynamic Axial Compressive Load* 1 Makoto Miyazaki* 2 and Hideaki Negishi* 3 Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Chofu , Japan Buckling, impact resistance and energy absorption of dynamic axial compressed aluminum square tube are discussed. Numerical analysis of the deformation of the square tube is made by a finite element method. The result shows that ripples of buckling are produced in the surfaces of the tube wall when the striking mass reaches to a certain value. The wave pattern on the deformed tube wall of 1 mm thick is concave-convex pattern in adjoining surface, while that of 2 mm thick is convex pattern in all surfaces. Absorbed energy of the deformed tube increases in proportion to axial displacement of the tube. Experimental results agree approximately with those of the finite element method analysis. (Received January 15, 23; Accepted June 3, 23) Keywords: square tube, impact test, numerical analysis, deformation-load property, absorbed energy 1. Introduction Square tube has been used for a framework and reinforcement member of the structures. The behavior of dynamic deformation must be studied in order to use square tube as an impact absorption member. The study of the dynamic deformation is mentioned in the following. Meng et al. 1) carried out an experiment and a plastic hinge analysis on large deformation mechanism of the square tube. Okamoto et al. 2) carried out the experiment on axially compressed circular tube and steel square tube, and compared the static deformation and the dynamic deformation by the plastic hinge analysis. Sawairi et al. 3) examined the influence of the corner radius on deforming behavior of axially compressed square tube by the finite element method. About the static deformation of the square tube, the examination of buckling mode of the aluminum square tube was carried out by Utsumi and Sakaki. 4) Authors 5) examined the deforming behavior of axially compressed thin square tube. However, the deforming behavior and the deformation energy have not been clarified. This paper deals with the deformation and energy absorption of axially compressed aluminum square tube. 18 mm Fig. 1 Drop-hammer testing machine. Guide shaft Striking mass Support frame Grooved plate Specimen Base 2. Experiment 2.1 Procedure A drop hammer testing machine, shown in Fig. 1, is used for dynamic axial compression of the square tube specimen. The drop hammer weight is 7.92 kg and its impact velocity depends on the falling height of the hammer. The impact velocities v are changed from 1.4 to 5.4 m/s. The ends of the specimen are fixed into the groove on the steel plate (2.5 mm width, 5 mm depth). The specimen, shown in Fig. 2, is an aluminum square tube (JIS A663 T5, 4 mm width, 1 mm or 15 mm length, 1 mm or 2 mm thickness) and it is annealed for 1 hour at 673 K. Material properties are shown in Table 1. Corner radius R of the aluminum square tube is * 1 This Paper was Originally Published in Japanese in Journal of Japan Institute of Light Metals, 52-7 (22) * 2 Researcher, The University of Electro-Communications. * 3 Emeritus Professor, The University of Electro-Communications. w t w = 4 l =1,15 t =1., 2. Fig. 2 Shapes and dimensions of specimens. Table 1 Material Properties. oung s modulus E/GPa 69 Poisson s ratio.33 Density /kg/m 3 2: F value F/MPa 222 n value n.25

2 Deformation and Energy Absorption of Aluminum Square Tubes with Dynamic Axial Compressive Load 1567 R :2 mm. The axial strain of the specimen was measured by the lattice of 4 mm interval described on the surface of the specimen. 2.2 Results Figures 3 and 4 show examples of the dynamically deformed tube. Deformation shape of 1 mm thickness tube is concave-convex in adjoining surfaces at an impact velocity of 1.4 m/s. The tendency appeared markedly at impact velocities of 2.8 and 3.7 m/s. The buckling deformation of 2 mm thickness tube was observed at an impact velocity of 2.8 m/s. On the impact velocity of 3.7 m/s, the convex shapes appeared in all surfaces of the tube. The tendency was observed markedly at the impact velocity of 5.4 m/s. In the square tube of 1 mm thickness and 1 mm length, the partial buckling was generated in the center of the axial direction of the tube. The buckling of 2 mm thickness tube was generated on the edges. In this experiment, the whole tube crushing was not observed in both of the thicknesses. (1) 1.4 m/s (2) 2.8 m/s (3) 3.7 m/s Fig. 3 Dynamically deformed specimens (t ¼ 1 mm, l ¼ 1 mm). (1) 2.8 m/s (2) 3.7 m/s (3) 5.4 m/s Fig. 4 Dynamically deformed specimens (t ¼ 2 mm l ¼ 1 mm).

3 1568 M. Miyazaki and H. Negishi 3. Numerical Analysis 3.1 Method The numerical analysis is carried out by non-linear structure analysis program (Marc 2) and pre-post processor (Mentat 2). The nodes in the edge of the square tube are fixed except for an axial direction of the impact edge. The boundary condition is similar to one of the experiments. The tube (4 mm width, 1 mm length, 1 mm or 2 mm thickness) is discretized into 1344 bilinear four-node shell elements. The tube (4 mm width, 15 mm length, 1 mm or 2 mm thickness) is discretized into 234 bilinear four-node shell elements. The hammer (12 mm 12 mm 4 mm) is an un-discretized three-dimensional, eight-node, firstorder, isoparametric element. The deformed tube is regarded as an isotropic material following to von-mises yield condition and the flow stress-strain relationship is eq. (1) because the effect of the strain rate of the aluminum is smaller than other materials like iron, etc. The strain rate in this experiment was 5 s 1. ¼ F" n ð1þ The time step width is 17.5 ms in this analysis. The Newton- Raphson method and updated Lagrangian formulation are used as the solution methods of the non-linear equation, and the Newmark of implicit solution time-integration method is used for the analysis of dynamic deformation. The impact velocities v are changed from 1.4 to 7.5 m/s. 3.2 Results Final deformations of the square tube for various impact velocities are shown in Figs Strain distributions in buckling region are shown in Figs. 9 and 1. Strain-time curve in buckling region is shown in Figs. 11 and 12. In the case of 1 mm thickness tube, shown in Figs. 5 and 6, the irregular pattern on the surface of the tube is a concaveconvex pattern on the adjoining surface. When the impact velocity is high, the second buckling is generated in the adjacency part in the first buckling. As seen in Fig. 9, compressive strain near the corner of the tube is large compared to that of the other part of the tube. In the case of 1 mm thickness tube, Face A has a convex surface and Face B has a concave surface. As seen in Fig. 11, strain near the corner of the tube in the beginning of the deformation is small Fig. 5 Dynamically deformed shapes obtained by FEM (t ¼ 1 mm, v ¼ 2:8 m/s, l ¼ 1 mm). Fig. 6 Dynamically deformed shapes obtained by FEM (t ¼ 1 mm, v ¼ 7:5 m/s, l ¼ 1 mm). Fig. 7 Dynamically deformed shapes obtained by FEM (t ¼ 2 mm, v ¼ 5:4 m/s, l ¼ 1 mm). Fig. 8 Dynamically deformed shapes obtained by FEM (t ¼ 2 mm, v ¼ 7:5 m/s, l ¼ 1 mm).

4 Deformation and Energy Absorption of Aluminum Square Tubes with Dynamic Axial Compressive Load Experiment Analysis.1.2 Face A Corner Face B Distance from the corner, d / mm Time, T / ms Fig. 9 Axial strain distribution along the hill and valley of a concaveconvex surface (t ¼ 1 mm, v ¼ 2:8 m/s, l ¼ 1 mm). Fig. 11 Axial strain-time curve at the center and corner of Face A and Face B(t ¼ 1 mm, v ¼ 2:8 m/s, l ¼ 1 mm) Distance from the corner, d / mm Experiment Analysis Fig. 1 Axial strain distribution along the hill of a convex surface (t ¼ 2 mm, v ¼ 5:4 m/s, l ¼ 1 mm). compared to that of the other part of the tube. With the deforming, Face A changes to tensile strain. It is considered that the buckling is produced in the side. After the side is buckled, the axial compressive strain increases greatly near the corner. It is considered that the buckling is produced in the corner. The buckling happens first in the side, and then another buckling happens near the corner. In the 2 mm thickness tube, shown in Figs. 7 and 8, the convex shape appeared in all surfaces at the end of the tube. In the case of 2 mm thickness, one side in adjoining surface is Face A, and the other side is Face B. As seen in Fig. 1, compressive strain near the corner of the tube is small compared to that of the other part of the tube, because buckling shape is convex in all surfaces. As seen in Fig. 12, after the compressive strain reaches to the peak, it changes to the tensile strain in the side. It is considered that the buckling is produced in the side. Unlike the case of the 1 mm thickness tube, the deformation of the 2 mm thickness tube is not wavily generated. The first buckling happened in the edge, and a little later the second buckling is produced in the opposite edge. Even under other conditions, the strain distributions that are obtained with the experiment and analysis are almost the same. The size and kind of element seems to be appropriate because experimental results agree approximately with those of the finite element method analysis. In the case of the 1 mm thickness tube and 2 mm thickness tube, there is a difference in the deformation shape. The deformation near the corner is simplified as shown in Fig. 13. The continuous line of the figure shows before the deformation of the tube, and the broken line of the figure shows after the deformation of the tube. The deformation of Fig. 13(a) is obtained by greatly twisting of the corner. It is the deformation of 1 mm thickness of the tube. The deformation of Fig. 13(b) is the deformation obtained by the extension of Time, T / ms the side without twisting in the corner. The torsional rigidity in the corner is given in eq. (2). ¼ GI p ¼ G 1 6 t4 G is modulus of transverse elasticity and I p is polar moment of inertia of the area. In this case, I p is t 4 =6. From eq. (2), the polar moment of inertia of the area in the corner becomes large, when the thickness is large. The corner torsional rigidity increases. The torsional rigidity in the corner of 2 mm thickness tube is larger than 1 mm thickness tube 16 times. The torsional rigidity in the corner of the 1 mm thickness tube becomes smaller than torsional rigidity in the corner of the 2 mm thickness tube, and the corner of the 1 mm thickness tube becomes easy to twist. Therefore, 1 mm thickness tube becomes a concave-convex pattern on the adjoining surface. The torsional rigidity in the corner seems to contribute greatly to the decision of the deformation shape. 4. Energy Absorption Face A Corner (Face B) Fig. 12 Axial strain-time curve at the center and corner of Face A and Face B(t ¼ 2 mm, v ¼ 5:4 m/s, l ¼ 1 mm). Fig. 13 (a) Before deformation Afrer deformation (b) Deformation patterns in corner part of square tube. The relationship between the axial displacement and absorbed energy are shown in Figs. 14 and 15. Q is an ð2þ

5 157 M. Miyazaki and H. Negishi Absorbed energy, Q / J Axial displacement, x / mm energy absorbed by a whole square tube. The energy absorption quantity was calculated from the plastic working quantity to the end of deformation. In the case of 1 mm and 2 mm thickness, absorbed energy of the impact load by the tube deformation increases in proportion to the axial displacement of the tube. There is no change on this tendency, even if the axial compression deformation increases. If the thickness and the axial maximum displacement are same, absorbed energy becomes the same in the case of different axial length. It is shown that the influence of the difference of the axial length on the energy absorption characteristic is small when the square tube normally buckles. Energy absorption quantities at each impact velocity is shown in Tables 2 and 3. Q b is energy absorbed by the buckling deformation region of the square tube. When weight collides with the tube, the value of energy agrees approximately with the value of Q shown in Tables 2 and 3. In the initial stage of deformation, the energy is absorbed by the whole square tube. The energy absorption quantity in the buckling deformation region increases, as the buckling is generated, and as the deformation increases. The effectiveness as impact absorption member of the aluminum square tube is shown, because the energy is greatly absorbed in the buckling deformation region and the deformation has been partially carried out. 5. Conclusions Axial length 1 mm 15 mm Fig. 14 Relationship between absorbed energy Q and axial displacement x (t ¼ 1 mm). Absorbed energy, Q / J Axial displacement, x / mm Axial length 1 mm 15 mm Fig. 15 Relationship between absorbed energy Q and axial displacement x (t ¼ 2 mm). From the experiment and numerical simulation, the following conclusions were obtained. (1) In the case of the tube of thin wall, the deformation shape is concave-convex in adjoining surfaces at the center of the axial direction of the tube, and the deformation is wavily generated. (2) In the case of the tube of thick wall, the convex shape appeared in all surfaces at the end of the tube. The first buckling happened in the edge, and a little later the second buckling is produced in the opposite edge. (3) The buckling happens first in the side, and then another buckling happens near the corner. (4) The absorbed energy of the impact load by the tube deformation increases in proportion to the axial displacement of the tube. (5) The square tube of thin wall is effective for the impact absorption member because the impact is absorbed by the partial buckling and the deformation is wavily generated. REFERENCES Table 2 Energy Absorption (t ¼ 1 mm). v/ms 1 l/mm Q/J Q b /J Q: Absorbed energy Q b : Absorbed energy at buckling region Table 3 Energy Absorption (t ¼ 2 mm). v/ms 1 l/mm Q/J Q b /J ) Q. Meng, S. T. S. Al-Hassani and P. D. Soden: Int. J. Mech. Sci. 25 (1983) ) S. Okamoto, T. Tsuta, J. Bai and M. Doi: JSME 71st Fall Annual Meeting B93-63 (1993) ). Sawairi, M. Gotoh and M. amashita: Proc. of 1999 Japanese Spring Conf. For the Technology of Plasticity, (1999) ) N. Utsumi and S. Sakaki: Proc. of 1999 Japanese Spring Conf. For the Technology of Plasticity, (1999) ) M. Miyazaki, H. Endo and H. Negishi: J. Mater. Process. Technol (1999)