A suitable criterion for precise determination of incipient necking in sheet materials

Abstract

Forming limit diagram (FLD) is a measure of the formability of a sheet material. The major-minor strain pairs that are closest to the neck on multiple specimens of various strain paths are utilized to construct a boundary between safe and unsafe zones. The challenge to obtain the FLD is the determination of incipient necking. Three approaches to determine the limit strains have been investigated and compared in this research in order to establish the optimal one for implementation: (1) commonly used Bragard criterion (ε1) Br periodic grids; (2) tracking the region of large local strains from strain history to locate the instance when critical major strain (ε1)cr happens; (3) post-processing of strain history to locate the inflection in the major strain rate curve (ε̈ 1)max of localization. The last criterion of inflection in strain rate (ε̈1)max., carries both a numerical and a physical meaning towards developing an understanding of flow localization, formability and fracture.