Strain localisation in biaxially stretched sheets containing compact defects—II: Analysis using a finite element model

Abstract

The development of strain localisation in a biaxially stretched sheet of work hardening material which contains a regular array of axisymmetric defects has been analysed by the finite element method. The defects were circular regions of reduced initial thickness and their spacing was close enough to permit interaction of the individual fields of strain concentration, leading to the formation of coherent regions of strain localisation across the sheet. Numerical results for the effects of defect severity on limit strains given by the new model are compared with those given by Marciniak and Kuczynski's long groove model. When failure is assumed to coincide with completed localisation, the forms of the relationships between limit strains and the applied strain state predicted by the two models are closely similar but, in order to give similar magnitudes of the limit strains, the defect severities and the defect strains required in the axisymmetric defect model are much larger than those in the long groove model. For this reason, when defect strains are limited by fracture, the strain state dependencies predicted by the two models can be distinctly different. For the case of a typical drawing quality low-carbon steel, the predictions of the axisymmetric defect model are in much closer accord with experimental values than are those of the long groove model.