Plastic Flow Properties in Relation to Localized Necking in Sheets

Abstract

Considerable interest exists in understanding the levels of maximum useful strains achievable prior to localized necking (forming limits) and their dependence on the imposed stress-state. Marciniak’s model of imperfection growth has successfully explained the rise in forming limit as the imposed strain-ratio (e2/e1) is increased from zero (plane strain) toward unity (balanced biaxial tension). Experimental studies on formability of various materials have, however, revealed basic differences in behavior, such as the “brass-type” and the “steel type”, exhibiting respectively, zero and positive dependencies of forming limit upon the strain-ratio. Such results cannot be reconciled without proper attention to the details of strain hardening and strain-rate hardening behaviors of these materials, particularly as functions of strain and strain-ratio. A review of these properties for several materials will be presented in an attempt to show their importance on the necking behavior. Furthermore, the dependence of the patterns of behavior upon the mode of stretching (in-plane and punch stretching) is discussed. Some results of a Marci niak-type model of material imperfection are also considered.