On the expansion of a circular hole in an orthotropic elastoplastic thin sheet

The expansion of a circular hole in an orthotropic sheet of AA6022-T4 is examined using a combination of experiments and analysis. This deformation mode is accomplished by stretching a hole at the bottom of a cup during drawing in a hydraulic press with a flat-headed punch. The strain fields are acquired continuously throughout the hole-expansion experiment, using stereo-type Digital Image Correlation. This reveals that despite the axisymmetry of the set-up, non-uniform thinning is observed around the hole throughout the expansion, due to the anisotropy of the material. The greatest thinning occurs at +45 degrees from the rolling direction. The strains that develop at the hole periphery are significantly higher than the uniform elongation in uniaxial tension (true strain of 0.37 vs. 0.18, respectively). Furthermore, the strain paths change from uniaxial tension around the hole to plane-strain tension and biaxial stretching farther away. The experiments are simulated using finite element analysis. The orthotropy of the material is modeled with the non-quadratic anisotropic yield criterion Yld2000-2D, calibrated by uniaxial tension, plane-strain tension and disk compression experiments. Special attention is placed on the identification of the large-strain hardening curve, which is accomplished by acquiring the strain fields inside the growing neck in uniaxial tension, and using them to minimize the difference between internal and external work. For the material at hand, the Voce hardening law is found to provide the best fit, while the impact of plastic anisotropy on the identification is negligible. It is shown that this modeling framework not only reproduces the structural behavior (e.g., the punch force-displacement) very well, but it also provides accurate predictions of the thinning variation around the hole.