Stress distribution during neck formation : an approximate theory

In this paper we investigate the effects of deformation of a metal specimen, which is either a plate or a cylindrical rod in our case. In particular we study neck formation in tensile loading of a plastic metal. We try to generalize the work of Bridgman, who considered a purely two-dimensional geometry, to an effective theory that takes into account some essential three dimensional characteristics. That extending the description of neck formation to three dimensions is necessary was illustrated by recent experimental findings of [1]. We have studied existing models from the literature that describe necking for plates and cylinders to identify the consequences of the crucial assumption of uniform in-plane stress. We also developed a new model that we have not yet been able to analyze. Finally, using work of [4] in which a power law relation between the von Mises stress and the effective strain is used, a perturbation analysis for a simple flat geometry was performed. The perturbation analysis offers a good starting point for generalizing the work of Bridgman to three dimensions. Keywords: Neck formation, von Mises stress, tensile pulling, plane stress assumption