International Journal of Material Forming

, Volume 12, Issue 2, pp 211–221 | Cite as

Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

  • Mohamed Ben BettaiebEmail author
  • Farid Abed-Meraim
  • Xavier Lemoine
Thematic Issue: Advances in Material Forming Simulation


A number of parts and components involved in the automotive industry are made of thin bent sheets, which are subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. Unfortunately, the classical predictions based on the conventional concept of Forming Limit Diagram (FLD) are no longer relevant when the strain distribution is heterogonous over the sheet thickness. Therefore, this conventional FLD concept is not capable of accounting for the effect of out-of-plane stresses on the onset of localized necking. The aim of the present contribution is to propose an extension of the well-known Marciniak–Kuczynski approach to simultaneously account for the effect of curvature and normal stress on formability prediction. The new developed tool allows predicting the limit strains for the whole range of strain paths. The mechanical behavior of the studied sheets follows the rigid–plastic flow theory. Through numerical results, it is shown that both curvature and normal stress tend to increase the formability limit of the sheet metal.


Forming limit diagrams Localized necking Flow theory Out-of-plane stress Curvature Marciniak–Kuczynski approach 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2017

Authors and Affiliations

  • Mohamed Ben Bettaieb
    • 1
    • 2
    Email author
  • Farid Abed-Meraim
    • 1
    • 2
  • Xavier Lemoine
    • 1
  1. 1.LEM3, UMR CNRS 7239 - Arts et Métiers ParisTechMetz Cedex 3France
  2. 2.DAMAS, Laboratory of Excellence on Design of Alloy Metals for low-mAss StructuresUniversité de LorraineNancyFrance

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