Failure in thin sheets stretched over rigid punches

Abstract

Criteria for diffuse and local necking in sheet metals stretched over a hemispherical punch have been developed. During stretching, a peak develops in the distribution of strain across the dome. This peak is a ring of thinned material around the pole which moves outward radially with continued deformation. The present approach essentially focuses on the loading rate of the region bounded by this ring of maximum thinning referred to here as thecrown. While diffuse instability is identified with a vanishing rate of crown loading, local necking is associated with the onset of a rapid rate of thinning under falling crown load. The principal surface strains were measured from incremental stretching of several different materials and time dependent constitutive relations were used to predict the instability strains. Such predictions agree with experimentally observed forming limits defined by the onset of visible necking and provide an understanding of the failure of biaxially stretched sheets deformed by a rigid punch. Since no satisfactory plasticity analyses have been developed to predict the strain distribution during punch stretching, the empirical input to the present instability criterion is required.