On the susceptibility to localized necking of defect-free metal sheets under biaxial stretching

Since the introduction of the concept of the forming-limit diagram to represent acceptable limit strains during sheet metal forming by Keeler and Backofen in 1963, it has become a major research topic and a considerable number of experimental and theoretical studies have been carried out. In most of the theoretical models, a type of defect is introduced and accommodated into the theoretical formulation. However, these models have met with only partial success. Moreover, in real materials, there do exist various types of defects, and their effects on limit strains may be overlapping and interacting. A single theoretical model that can fully explain or predict the formation of localised necking in a wide range of materials seems unrealistic. In this paper, a model based on the upper-bound theorem has been proposed to assess the susceptibility to localized necking of defect-free sheets under biaxial stretching. Without assuming a defect, the effects of the work hardening, anisotropy and geometry of a sheet on the limit strains have been analyzed. The significance of the findings is discussed.