Plastic Instability in Simple Stretching of Sheet Metals

Abstract

The plastic instability was examined for stretching a plane flat sheet by in-plane tensile principal stresses. Limiting equilibrium or development of nonuniform strains defines the onset of plastic instability. Under dead loading the Swift theory gives the conditions for limiting equilibrium, while it results in the condition for the failure of uniqueness for given strain paths. When the initial nonuniformity of the properties and dimensions in the sheet is considered, the Dorn maximum load criterion is applicable for the condition of plastic instability. The optimum paths along which the maximum strains can be achieved before instability takes place were obtained and the limiting maximum strains was calculated along these paths for the Dorn criterion and for the Swift theory.