An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis

Abstract

In this paper, formula derivation for bifurcation analysis based on a constitutive model including Hill 48 yield criterion with normal anisotropy of a pointed vertex on subsequent yield loci to predict the entire forming limit diagram (FLD) is carried out. Proportional loading, total deformation theory of plasticity, and power law relation are assumed. Predicted limit strains for Hill’s zero and minimum extension of localized neck orientation is derived. The dominancy of zero extension and minimum extension on the left-hand side of FLDs for different work hardening components and r-values are investigated in detail. An implicit four order rational function equation for major strain, which preferred that the orientation of neck correspond to minimum value of limit strain, is found by a developed optimization method. Optimized predicted limit strains for typical work hardening components and different r-values are obtained and discussed. Limit strains vary directly on the left and reversely on the right-hand side of FLD when r-value increases. Comparison between the predicted and experimental results exhibits a better agreement compared with those from the isotropic material. In addition, on the left-hand side, the resulted prediction limit strains represent a full dependency to assumed yield criterion. A comparison between the current work and Chow et al. results are performed and discussed in detail.