Abstract
Localized necking in sheet metal has been examined for strain paths between uniaxial tension and plane strain (i.e., the negative minor strain region of a forming limit diagram). The behavior of sheet with preexisting imperfections has been analyzed and is contrasted to that free of imperfections. In particular, it is shown that the size and orientation of an imperfection is critical in determining whether or not localized necking is initiated along the imperfection. The influence of strain hardening, strain rate hardening, and plastic anisotropy on localized necking of an imperfect sheet is also examined. One of the most significant conclusions obtained from present analysis and from a reexamination of Hill’s theory is the prediction of a critical thickness strain criterion for the onset of localized necking at negative minor strains, regardless of whether or not an imperfection is present. The critical thickness strain criterion is observed in Ti alloys, Al alloys, steels, and brass.
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