Stress State Analysis of Radial Stress Superposed Bending

  • Rickmer MeyaEmail author
  • Christian Löbbe
  • A. Erman Tekkaya
Regular Paper


Radial stress superposed bending is a sheet metal bending process, which superposes predetermined radial stresses. Stress superposition is mandatory to enable the reduction of the triaxiality in bending, resulting in delayed damage evolution and an improved product performance. The knowledge of the stress state is essential for damage-controlled bending as the triaxiality is the driving force for the void evolution. To control the stress state in radial stress superposed bending, an additional counter force responsible for the pressure in the outer fiber is applied. To predict the effect of the counter force on the radial stress and the triaxiality an analytical model is proposed. The prediction of the reaction forces in the system is required for the process design and for the calculation of the stress superposition. The stress state for plane strain bending with stress superposition is derived, and pressure calculations are made using the theory of Hertz. The model and the assumptions are verified in numerical and experimental studies for various counter pressures and bending ratios. Finally, a discussion of the load path depending on the transient counter pressure is carried out and experimental evidence for a inhibited damage evolution due to stress superposition is given.


Damage Process design Sheet metal bending Stress state analysis Stress superposition 

List of Symbols


Plastic strain


Principal stresses


Flow stress


Mean stress


Von Mises equivalent stress


Stress invariants


Deviatoric stress invariants


Stress triaxiality


Normalized third stress invariant

\(\bar{\theta }\)

Lode angle parameter


Lode parameter


Friction coefficient


Normal forces


Tangential forces


Contact angle of forces


Loaded bending angle


Punch radius


Outer bending radius


Distances between forces


Sheet thickness


Bending moment


Contact width of the radial stress


Contact pressure


Sheet width


Punch stroke



The investigations are kindly supported by the German Research Foundation in context of the Collaborative Research Centre CRC/Transregio 188 “Damage-Controlled forming processes”, project A05. We thank Mr. Carl Kusche for his support in recording the SEM-micrographs.


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  • Rickmer Meya
    • 1
    Email author
  • Christian Löbbe
    • 1
  • A. Erman Tekkaya
    • 1
  1. 1.Institute of Forming Technology and Lightweight ComponentsTU Dortmund UniversityDortmundGermany

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