An anisotropic model with linear perturbation technique to predict HCP sheet metal ductility limit

Abstract

In this paper, hexagonal closed packed (HCP) sheet metal ductility for a viscoplastic material is analyzed by using a linear perturbation technique. It can be used for the analysis of localized necking. This technique is used to perturbate the material behavior in a rate-dependent formulation by superimposing a perturbation to the basic flow, whose stability or instability is characterized by the increasing or decreasing of the perturbation. Hardening and initial anisotropic parameters are fitted by experimental results from the literature. In this investigation, Cazacu yield function is used to predict the forming limit diagrams (FLDs) of HCP sheet metals. The coupling between analytic perturbation method and the behavior modelling is provided by an efficient implicit algorithm to solve the constitutive equations. After verifications and validations of the numerical simulations from the literature, the ductility limit of a particular HCP magnesium alloy is numerically predicted. A parametric study is presented to analyze the effect of instability and mechanical parameters, viscosity and distortion on the FLDs. Moreover, a comparative study between Marciniak and Kuckzynski ductility approach and linear perturbation technique is done in this contribution.