Predicting Tube Ovalization in Cold Bending: An Analytical Approach

Article Preview

Abstract:

Ovalization (or flattening) of tubes in cold bending operations causes dimensional inaccuracy that may lead to loss of fit-up and function of the formed product. The particular distortion mechanism is governed by radial bending stress components forcing the extremities of the tube section towards the neutral layer of the cross-section. Thus, the magnitude of distortions is limited by the instantaneous stiffness of the tube section upon plastic bending. In order to proactively consider tube ovalization in the product design process, it is necessary to develop a practical methodology that takes into account the impact of governing parameters such as material, tool and section geometries. In the present work, an analytical model of the ovalization problem has been developed using the deformation theory of plasticity. The results show that the diameter of the tube is the most important parameter with respect to tube ovalization, while the thickness of the tube section and the bending radius are of the same relative importance. The developed model indicates that strain hardening is the most important material parameter, whereas tube ovalization is nearly unaffected by the initial yield stress. The present model shows good correlation with a number of experiments.

You might also be interested in these eBooks

Info:

Periodical:

Key Engineering Materials (Volumes 651-653)

Pages:

1146-1152

Citation:

Online since:

July 2015

Export:

Price:

* - Corresponding Author

[1] S. P. Timoshenko, Bending Stresses in Curved Tubes of Rectangular Cross-Section. Trans. ASME 45, 135 (1923).

Google Scholar

[2] L. G. Brazier, On the Flexure of Thin Cylindrical Shells and other Thin, Sections. Proc. R. Soc. Lond. Math. Phys. A116, 104 (1927).

Google Scholar

[3] R. Hill, The Mathematical Theory of Plasticity. Oxford Science Publications, 287, Oxford (1950).

Google Scholar

[4] C. S. Ades, Bending Strength of Tubing in the Plastic Range. J. Aero. Sci. 24, 605 (1957).

Google Scholar

[5] S. Gellin, The Plastic Buckling of Long Tubes under Combined Bending and Pressure Loads. Int. J. Solids Struct. 10, 397 (1980).

Google Scholar

[6] O. Fabian, Elastic-Plastic Collapse of Long Tubes under Combined Bending and Pressure Loads. Ocean Engng. 8, 295 (1981).

DOI: 10.1016/0029-8018(81)90027-5

Google Scholar

[7] P. K. Shaw and S. Kyriakides, Inelastic Analysis of Thin-Walled Tubes under Cyclic Bending. Int. J. Solids Struct. 21, 1073 (1985).

DOI: 10.1016/0020-7683(85)90044-7

Google Scholar

[8] S. Kyriakides and G. T. Ju, Bifurcation and Localization Instabilities in Cylindrical Shells under Bending¾I. Experiments. Int. J. Solids Structures 29, 1117 (1992).

DOI: 10.1016/0020-7683(92)90139-k

Google Scholar

[9] G. T. Ju and S. Kyriakides, Bifurcation and Localization Instabilities in Cylindrical Shells under Bending¾II. Predictions. Int. J. Solids Structures 29, 1143 (1992).

DOI: 10.1016/0020-7683(92)90140-o

Google Scholar

[10] S. R. Reid, T. X. Yu and J.L. Yang, Hardening-Softening Behaviour of circular Pipes under Bending and Tension. Int. J. Mech. Sci. 36, 1073 (1994).

DOI: 10.1016/0020-7403(94)90059-0

Google Scholar

[11] E. Corona and S. P. Vaze, Buckling of Elastic-Plastic Square Tubes under Bending. Int. J. Mech. Sci. 38, 753 (1996).

DOI: 10.1016/0020-7403(95)00081-x

Google Scholar

[12] F. Paulsen and T. Welo, Cross-sectional Deformations of Rectangular Hollow Sections in Bending: Part II ¾Analytical Models. Int. J. Mech. Sci. 43, 131 (2001).

DOI: 10.1016/s0020-7403(99)00107-1

Google Scholar

[12] F. Paulsen and T. Welo, Cross-sectional Deformations of Rectangular Hollow Sections in Bending: Part II ¾Analytical Models. Int. J. Mech. Sci. 43, 131 (2001).

DOI: 10.1016/s0020-7403(99)00107-1

Google Scholar

[13] W. Wu, P. Zhang, X. Zeng, L. Jin, S. Yao and Luo A.A., Bendability of the wroght magnesioum alloy AM30 tubes using a rotary draw bender, Mater. Sci. Eng. A, 486 (1-2), pp.596-601 (2008).

DOI: 10.1016/j.msea.2007.09.033

Google Scholar

[14] A. Mentella and M. Strano, Rotary Draw Bending of Small Diamater Copper Tubes: Predicting the Quality of the Cross Scetion, Proc. IMechE PartB: J. Eng. Manuf., 226, pp.267-278 (2012).

DOI: 10.1177/0954405411416306

Google Scholar

[15] H. Li, H. Yang. Z.Y. Zhang, G.J. Li, N. Liu and T. Welo, Multiple instability-constrained tube bending limits, J. of Materials Processing Technology, 214 pp.445-455, (2014).

DOI: 10.1016/j.jmatprotec.2013.09.027

Google Scholar

[16] C. E. Greene, Graphical Method for the Analysis of Bridge Trusses, D. Van Nostrand Co. Inc., 35, New York (1875).

Google Scholar