Wrinkling of anisotropic metal sheets under deep-drawing: analytical and numerical study

Abstract

The onset of wrinkling in sheet metal forming is investigated using an analytical approach and finite element (FE) simulations. In both cases the yield criterion proposed by Ferron et al. [Int. J. Plast. 10 (1994) 431] for orthotropic sheets is employed. The analytical approach is developed on the basis of the bifurcation criterion developed by Hutchinson [J.W. Hutchinson, Plastic buckling, in: C.-S. Yih (Ed.), Advances in Applied Mechanics, vol. 14, 1974, pp. 67–144] for thin and shallow shells submitted to a biaxial plane stress loading. Wrinkling limit curves obtained with the bifurcation analysis are drawn for different orientations of the orthotropic axes with respect to the principal stress axes, assuming also different orientations with respect to the geometric axes of principal curvatures. The numerical simulations are performed with the FE code ABAQUS/Explicit. Experimental results of deep-drawing processes taken from the literature are also analysed to check the reliability of the wrinkling predictions obtained with the bifurcation analysis and with the FE simulations. Both analytical and numerical predictions compare reasonably well with experiments.