Hardening model of anisotropic sheet metal during the diffuse instability necking stage of uniaxial tension

Abstract

In order to determine the stress–strain response in the diffuse necking for low carbon steels, the evolution of the diffuse necking region and the distributions of stress and strain in the narrowest cross-section are analyzed comprehensively based on 3D-DIC and FE simulation. Three parabolic functions are adopted to simplify the diffuse necking deformation: the shape of the necking region is parabolic, the distributions of stress and strain in the narrowest cross-section are also parabolic. A hardening model for solving the uniaxial tensile true stress and strain in the diffuse necking is established. Uniaxial tensile tests of four kinds of low carbon steel sheets and three typical anisotropic directions have been carried out to verify the reliability of the developed model. The numerical simulation results show that the uniaxial tensile load–elongation curves based on the hardening model are in good agreement with the experimental results, with an error of less than 1.3%. The true stress and strain in the diffuse necking can be determined easily by interpreting the tensile curve and measuring the shape of necking region. It avoids the difficulty and time-consuming of the inverse methods. This study can provide a valuable reference for establishing theoretical models to acquire true stress–strain curves over large range of strains for anisotropic sheet metals.