Effects of the shape of a geometric defect and of interactions between defects on limit strains for biaxially stretched sheets

Abstract

The effects of the shape of an initial geometric non-uniformity on limit strains for a biaxially-stretched sheet are first studied. An elliptic imperfection having various ratios of major to minor axis is considered. It is shown that the standard M-K imperfection gives lower bounds to forming limit diagrams. Then interactions between geometrical non-uniformities are studied by considering separately interactions for single rows of imperfections, as well as for periodically-spaced imperfections. The importance of interactions is pointed out and the results show that such interactions may not always be neglected in sheet metal formability analyses. The material of the sheet is assumed to be incompressible, elastic-plastic and rate-insensitive. Assuming that the behavior of the sheet can be described by generalized plane-stress assumptions, a large strain-plane-stress finite-element program is developed. Results are presented using finite-strain versions of J 2 flow theory and J 2 deformation theory of plasticity.