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The estimation of material formability plays a central role in the design of metal forming processes. The present paper focuses on the phenomenon of necking in sheet metals which leads to undesirable localized straining and occurs when the sheet metal is subjected to monotonic or non-monotonic plastic tensile loading. In sheet metal forming diffuse and localized necking are distinguished. According to (Barata da Rocha et al., 1984¨C1985), in industrial stampings the maximum allowable straining is not determined by diffuse but by localized necking. Diffuse necking is characterized by contraction strains in both the width and the thickness directions of the sheet (Hosford and Caddell, 1993 W.F. Hosford and R.M. Caddell, Metal Forming ¨C Mechanics and Metallurgy, (second ed.), Prentice Hall (1993).  [Hosford and Caddell, 1993] and [Lian and Zhou, 1989] ). The neck develops gradually and considerable extension is still possible after the onset of diffuse necking. Finally, a condition will be reached where a sharp localized neck starts to form. The width of the localized neck is of the order of the sheet thickness. According to Hill (1952) and Lian and Zhou (1989) localized necking is based on zero strain along the necking band so that the onset of localized necking corresponds to a plane strain deformation mode. Barlat (1987) states that localized necking corresponds to exceeding a critical thickness strain and that the material¡¯s limiting strains under biaxial loading are associated to its thinning resistance
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