Elasto-Plastic Springback of Beams Subjected to Repeated Bending/Unbending Histories

  • Franc Kosel
  • Tomaz Videnic
  • Tadej Kosel
  • Mihael Brojan
Article

Abstract

This contribution investigated repeated elastoplastic pure plane bending/unbending process of beams made of material with an elastic-linear hardening rheological model. The attention is focused on beams with cross sections which have at least one axis of symmetry and are initially straight or have constant radius of curvature. Elastoplastic deflection states of beams after repeated bending/unbending process are determined using the large displacement theory. Experiments were conducted to verify the theory for beams made of aluminium alloy AA 5050-H38 with rectangular cross sections. It is shown that maximal relative difference between experimental and theoretical results in the case of a largely curved beams after repeated bending/unbending process is 1.27%.

Keywords

elastic-linear strain hardening model elastoplastic deformations repeated bending/unbending process springback 

References

  1. 1.
    G. Liu, Z. Lin, Y. Bao, and J. Cao, Eliminating Springback Error in U-Shaped Part Forming by Variable Blankholder Force, J. Mater. Eng. Perform., 2002, 11(1), p 64–70CrossRefGoogle Scholar
  2. 2.
    A. Jernberg, A Method for Modifying the Forming Tool Geometry in Order to Compensate for Springback Effects, 4th European LS-DYNA Users Conference, May 22-23, 2003 (Ulm, Germany), DYNAmore 2003, p E-III-45–E-III-54Google Scholar
  3. 3.
    M.L. Garcia-Romeu, J. Ciurana, and I. Ferrer, Springback Determination of Sheet Metals in an Air Bending Process Based on an Experimental Work, J. Mater. Process. Technol., 2007, 191(1–3), p 174–177CrossRefGoogle Scholar
  4. 4.
    F.J. Gardiner, The Springback of Metals, Trans. ASME, 1957, 79, p 1–9Google Scholar
  5. 5.
    W. Johnson and T.X. Yu, On Springback After the Pure Bending of Beams and Plates of Elastic Work-Hardening Materials III, Int. J. Mech. Sci., 1981, 23(11), p 687–695CrossRefGoogle Scholar
  6. 6.
    K.P. Li, W.P. Carden, and R.H. Wagoner, Simulation of Springback, Int. J. Mech. Sci., 2002, 44(1), p 103–122CrossRefGoogle Scholar
  7. 7.
    F. Yoshida and T. Uemori, A Model of Large-Strain Cyclic Plasticity and its Application to Springback Simulation, Int. J. Mech. Sci., 2003, 45(10), p 1687–1702CrossRefGoogle Scholar
  8. 8.
    J. Wang, V. Levkovitch, F. Reusch, and B. Svendsen, On the Modelling and Simulation of Induced Anisotropy in Polycrystalline Metals with Application to Springback, Arch. Appl. Mech., 2005, 74(11–12), p 890–899CrossRefGoogle Scholar
  9. 9.
    M.G. Lee, D. Kim, C. Kim, M.L. Wenner, R.H. Wagoner, and K. Chung, A Practical Two-Surface Plasticity its Application to Spring-Back Prediction, Int. J. Plast., 2007, 23(7), p 1189–1212CrossRefGoogle Scholar
  10. 10.
    D. Zeng and Z.C. Xia, A Modified Mroz Model for Springback Prediction, J. Mater. Eng. Perform., 2007, 16(3), p 293–300CrossRefGoogle Scholar
  11. 11.
    F. Cimolin, R. Vadori, and C. Canuto, Springback Compensation in Deep Drawing Applications, Meccanica, 2008, 43(2), p 101–113CrossRefGoogle Scholar
  12. 12.
    A.A. El-Domiaty and A.A. Elsharkawy, Stretch-Bending Analysis of U-Section Beams, Int. J. Mach. Tools Manuf., 1998, 38(1–2), p 75–95CrossRefGoogle Scholar
  13. 13.
    H.A. Al-Qureshi, Elastic-Plastic Analysis of Tube Bending, Int. J. Mach. Tools Manuf., 1999, 39(1), p 87–104CrossRefGoogle Scholar
  14. 14.
    K.C. Chan and S.H. Wang, Effect of Anisotropy on Springback of Integrated Circuit Leadframes, J. Mater. Eng. Perform., 1999, 8(3), p 368–374CrossRefGoogle Scholar
  15. 15.
    S. Baragetti, A Theoretical Study on Nonlinear Bending of Wires, Meccanica, 2006, 41(4), p 443–458CrossRefGoogle Scholar
  16. 16.
    Z. Dongjuan, C. Zhenshan, R. Xueyu, and L. Yuqiang, An Analytical Model for Predicting Springback and Side Wall Curl of Sheet after U-Bending, Comput. Mater. Sci., 2007, 38(4), p 707–715CrossRefGoogle Scholar
  17. 17.
    A. El Megharbel, G.A. El Nasser, and A. El Domiaty, Bending of Tube and Section Made of Strain-Hardening Materials, J. Mater. Process. Technol., 2008, 203(1–3), p 372–380CrossRefGoogle Scholar
  18. 18.
    M.G. Lee, J.H. Kim, K. Chung, S.J. Kim, R.H. Wagoner, and H.Y. Kim, Analytical Springback Model for Lightweight Hexagonal Close-Packed Sheet Metal, Int. J. Plast., 2009, 25(3), p 399–419CrossRefGoogle Scholar
  19. 19.
    R. Kazan, M. Firat, and A.E. Tiryaki, Prediction of Springback in Wipe-Bending Process of Sheet Metal Using Neural Network, Mater. Des., 2009, 30(2), p 418–423CrossRefGoogle Scholar
  20. 20.
    C.C. Chu, Elastic-Plastic Springback of Sheet Metals Subjected to Complex Plane Strain Bending Histories, Int. J. Solids Struct., 1986, 22(10), p 1071–1081CrossRefGoogle Scholar
  21. 21.
    J.S. Shu and C. Hung, Finite Element Analysis and Optimization of Springback Reduction: The “Double-Bend” Technique, Int. J. Mach. Tools Manuf., 1996, 36(4), p 423–434CrossRefGoogle Scholar
  22. 22.
    J.T. Gau and G.L. Kinzel, A New Model for Springback Prediction in which the Bauschinger Effect is Considered, Int. J. Mech. Sci., 2001, 43(8), p 1813–1832CrossRefGoogle Scholar
  23. 23.
    Y. Yao, M.W. Lu, and X. Zhang, Elasto-Plastic Behavior of Pipe Subjected to Steady Axial Load and Cyclic Bending, Nucl. Eng. Des., 2004, 229(2–3), p 189–197CrossRefGoogle Scholar
  24. 24.
    F. Kosel and I. Borštnik, Upogib nosilcev s konstantnim prerezom v elasto-plastičnem območju (Bending of Beams with the Constants Cross Sections in the Elastoplastic Domain), Strojniški vestnik (J. Mech. Eng.), 1979, 25(9–10), p 205–208 (in Slovene)Google Scholar

Copyright information

© ASM International 2010

Authors and Affiliations

  • Franc Kosel
    • 1
  • Tomaz Videnic
    • 1
  • Tadej Kosel
    • 1
  • Mihael Brojan
    • 1
  1. 1.Laboratory for Non-Linear Mechanics, Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia

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