Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal

Abstract

A bifurcation analysis of forming limits for an orthotropic sheet metal is presented in this paper. The approach extends Stأ¶ren and Rice's (S–R) bifurcation analysis for isotropic materials, with materials following a vertex theory of plasticity at the onset of localized necking. The sheet orthotropy is represented by the Hill’48 yield criterion with three rvalues in the rolling (r0), the transverse (r90) and the diagonal direction (r45). The emphasis of the study is on the examination of rvalue effect on the sheet metal forming limit, expressed as a combination of the average rvalue raverage and the planar anisotropy (خ”r). Forming limits under both zero extension assumption and minimum extension assumption as well as necking band orientation evolution are investigated in detail. The comparison between the experimental result and predicted forming limit diagram (FLD) is presented to validate the extended bifurcation analysis. The rvalue effect is observed under uniaxial and equalbiaxial loadings. However, no difference is found under plane strain condition in strainbased FLD which is consistent with Hill's theory. The force maximum criterion is also used to analyze FLD for verification.