Localized necking of sheet metal under the biaxial stretching condition

Abstract

To account for the localized necking of sheet metal under the biaxial stretching condition, a theoretical model of localized necking was proposed. To develop the model, it was assumed that the deformation of sheet metal under biaxial stretching becomes locally inhomogeneous after the onset of diffuse necking due to the pre-existing imperfections, and thereby the local elements of the sheet undergo the transition of loading path. Based on the assumed condition, the onset condition of localized necking was identified. The proposed model was combined with particular constitutive equations to provide its application cases, where Hill's theory of localized necking was adopted together to cover non-biaxial stretching paths. Material properties and the forming limit strains of the aluminum alloy (Al6014-T4) sheet were characterized and compared with the limit strains obtained from the proposed model. Theoretical limit strains produced by the original M−K model and the MMFC were also compared with those of the proposed model and the experiments. With the advanced constitutive model, the proposed model well captured the distribution of experimental limit strains of the Al alloy sheet under biaxial stretching. The sheet instability was identified in terms of the instantaneous N-value of the work hardening model.