Geometric models of internal shape change as Shear Bands Form during Plane Strain Extension

Abstract

This paper systematically presents geometric models for describing internal shape change during plane strain extension of sheet. The models describe the geometry of plastic flow localization during sheet necking and formation of sample-scale shear bands within the neck. The emphasis is toward identifying three-dimensional, solid element models that correctly describe (1) the heterogeneous initiation of simple shearing flow, inside a band that occupies just a small fraction of the sheet thickness, (2) the gradual growth of bands of simple shearing across the sheet cross section, and (3) the development of a variety of patterns of sample-scale shear bands before sheet fracture. Models are identified that agree with experimental evidence. The geometry of these models provides quantitative links between flow localization throughout a deforming sample and changes in microscopic or crystal-scale flow behavior.