Production Engineering

, Volume 13, Issue 2, pp 201–209 | Cite as

Production of bistable fully closed metallic shells by introducing residual stresses during bending processes

  • Pavlo PavliuchenkoEmail author
  • Marco Teller
  • Markus Grüber
  • Thomas Bremen
  • Gerhard Hirt
Production Process


Bistable fully closed metallic shells are of great interest as lightweight construction components, which could be transported without enclosure and unfolded at the construction place. The effect of bistability in metallic shell structures is achieved by a specific distribution of residual stresses over the shell thickness, which can be introduced by bending processes. So far no fully closed structures have been achieved in metallic shells. Hence, the aim of this paper is the identification of suitable bending radii combinations in order to produce a bistable shell with a fully closed tube shape in the deployed state. Therefore, a Finite Element (FE) model was established to determine whether bistability occurs in dependence on the bending radii. The numerical model indicates, that bistability can be achieved for 0.2 mm thick spring steel 1.1274 (AISI 1095) by applying two die-bending operations with small bending radii of 6–8 mm. Accompanying experiments with a closed-die incremental bending tool were performed. A good transferability of the numerical results regarding the occurrence of bistability and the calculated residual stresses is shown. For the second aspect, X-ray diffraction measurements of residual stresses were used for comparison. Finally, the present work presents a process route to generate a bistable shell with a fully closed tube shape structure in the deployed state, having a radius of 40.95 mm.


Residual stresses Shell structures Deployable structures Bistable shells 



We thank the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for funding within the priority program SPP 2013 “The utilization of residual stresses induced by metal forming” (DFG, project HI 790/57-1). The authors would also like to thank the Leibniz Institute for Materials Engineering (IWT) for conducting X-ray diffraction measurements of residual stresses.


  1. 1.
    Pellegrino S (2001) Deployable structures, Chap. 1: Deployable structures in engineering, CISM Courses and Lectures, No. 412, Springer, pp. 1–35Google Scholar
  2. 2.
    Groskopfs E (1969) Storable tubular extensible member device. Patent US3434674A, registered 5 May 1967, published 25 Mar 1969. De Havilland Aircraft of Canada LtdGoogle Scholar
  3. 3.
    Kebadze E, Guest S, Pellegrino S (2004) Bistable prestressed shell structures. Int J Solids Struct 41:2801–2820. CrossRefzbMATHGoogle Scholar
  4. 4.
    He X (2011) Bi-stable character of laminated cylindrical shells. Proc Eng 14:616–621. CrossRefGoogle Scholar
  5. 5.
    Galletly D, Guest S (2004) Bistable composite slit tubes. I. A beam model. Int J Solids Struct 41:4517–4533. CrossRefzbMATHGoogle Scholar
  6. 6.
    Galletly D, Guest S (2004) Bistable composite slit tubes. II. A shell model. Int J Solids Struct 41:4503–4516. CrossRefzbMATHGoogle Scholar
  7. 7.
    Guest S, Pellegrino S (2006) Analytical models for bistable cylindrical shells. Proc R Soc A 462: 839–854. MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Wolf G, Wolf M (2006) Metal strip. Patent DE202006004427U1, registered17 Mar 2006, published 19 Apr 2007. Cobra Bandstahl GmbHGoogle Scholar
  9. 9.
    Kang S, Kim Y, Kim K, Kwon D, Kim J (2014) Constitutive equations optimized for determining strengths of metallic alloys. Mech Mater 73:51–57. CrossRefGoogle Scholar
  10. 10.
    Totten G,‎ Inoue T, Howes M (2002) Handbook of residual stress and deformation of steel, Chap, 7. Measurement of Residual Stresses, ASM International, pp 99–117Google Scholar

Copyright information

© German Academic Society for Production Engineering (WGP) 2019

Authors and Affiliations

  • Pavlo Pavliuchenko
    • 1
    Email author
  • Marco Teller
    • 1
  • Markus Grüber
    • 1
  • Thomas Bremen
    • 1
  • Gerhard Hirt
    • 1
  1. 1.Institute of Metal Forming (IBF)RWTH Aachen UniversityAachenGermany

Personalised recommendations