Ductile fracture of metallic structures is often preceded by its loss of stability and sub-
sequent plastic flow localization. The instability could stem from either material soft-
ening due to void nucleation, growth and coalescence or due to structural effects such
as necking or shear band formation. The interplay between these two mechanisms in
determining the ductility of the structure is still obscure. The ductile fracture models
developed so far are phenomenological in nature, based on the attainment of a critical
damage parameter. The void interactions as a result of strain localization in the lig-
aments and subsequent instability is not been accounted for. Also classical plasticity
models using a smooth yield surface and the normality flow rule can not predict lo-
calized necking in thin sheets at realistic strain levels when both the in-plane principal
strains are tensile. In this thesis, localized necking of thin sheets subjected to biaxial
loading is analysed using the framework of Storen and Rice (1975). First, a closed form
solution for the critical hardening modulus for anisotropic sheets subjected to biaxial
stretching is developed, which is shown to predict realistic limit strains when the minor
strain in the plane of the sheet is negative. Next, a recently developed multi-surface
model for porous metal plasticity is used to show that the development of vertices on
the yield surface at finite strains due to microscopic void growth, and the resulting devi-
ations from plastic flow normality, can result in realistic predictions for the limit strains
for positive minor strains. The shapes of the forming limit curves predicted using an
instability analysis are in qualitative agreement with experiments. The effect of consti-
tutive features such as strain hardening and void nucleation on the predicted ductility
are discussed.