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Stress State Analysis of Radial Stress Superposed Bending

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

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.

Keywords

Damage Process design Sheet metal bending Stress state analysis Stress superposition 

List of Symbols

ε

Plastic strain

σii

Principal stresses

σf

Flow stress

σm

Mean stress

σvM

Von Mises equivalent stress

Ii

Stress invariants

Ji

Deviatoric stress invariants

η

Stress triaxiality

ξ

Normalized third stress invariant

\(\bar{\theta }\)

Lode angle parameter

L

Lode parameter

µi

Friction coefficient

Ni

Normal forces

Ti

Tangential forces

φi

Contact angle of forces

α

Loaded bending angle

rp

Punch radius

Rbo

Outer bending radius

si

Distances between forces

t

Sheet thickness

Mb

Bending moment

dr

Contact width of the radial stress

pr

Contact pressure

b

Sheet width

h

Punch stroke

Notes

Acknowledgements

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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