/octave-form

Forming Limit Diagram Post-Processing for Abaqus

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Octave Form

  • Deep drawing FLD deepdraw demo FLD legend
  • Hydroforming FLD hydroforming demo FLD legend

The Forming Limit Diagram (FLD) is a common tool in sheet metal forming.

The quality of the part is predicted by the strain imposed during the forming procedure.

Forming Limit Curve

The forming limit curve (FLC) determinated experimetally (e.g. ISO12004); analytical methods are usually only used as a starting point.

lib/flc.m can be used to generate the FLC, based on Marciniak–Kuczynski's theory (M-K).

Marciniak–Kuczynski's Model

For the M-K's hyphothesis the fracture of the metal sheet is caused by inhomogeneities in its thickness.

\left(\dfrac{\bar{\varepsilon}^{\textsc{\tiny{A}}}}{\bar{\varepsilon}^{\textsc{\tiny{B}}}}\right)^{n}\left(\dfrac{\dot{\bar{\varepsilon}}^{\textsc{\tiny{A}}}}{\dot{\bar{\varepsilon}}^{\textsc{\tiny{B}}}}\right)^{m}=\frac{^{\bar{\sigma}^{\textsc{\tiny{A}}}}!!/{\sigma{1}^{\textsc{\tiny{A}}}}}{^{\bar{\sigma}^{\textsc{\tiny{B}}}}!!/{\sigma{1}^{\textsc{\tiny{B}}}}}~~\textrm{f}~e^{\left( \bar{\varepsilon}^{\textsc{A}}\frac{\partial\bar{\sigma}^{\textsc{A}}}{\partial\sigma_{1}^{\textsc{A}}} - \bar{\varepsilon}^{\textsc{B}}\frac{\partial\bar{\sigma}^{\textsc{B}}}{\partial\sigma_{1}^{\textsc{B}}} \right)}

flc_mk(n, f, alpha, interactive, m, delta, fail, Ss, E1, E2)

...

By default the simulation uses the von Mises criterion, giving

Abaqus

  • .inp are parsed using the function abaqus_load and supported elements are S4/S4R;
  • .rpt are loaded using abaqus_report.

References

Z. Marciniak, K. Kuczyński & T. Pokora. "Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension". Int. J. of Mech. Sci, Vol.15, pp.789-800, 1973.