Determining Localized Necking in Polycrystalline Sheet Metals Using the Bifurcation Phenomenon in Strain Evolution

Abstract

The forming limit is an important failure criterion for polycrystalline sheet metals when approving the forming process. Recent developments in strain measurement technology, e.g., digital image correlation (DIC), enable the strain evolution to be captured continuously and accurately. This new technology would improve the forming limit measurements if the onset of the necking detection method was developed accordingly. This paper proposes a new method based on the bifurcation phenomenon in strain evolution to detect the onset of localized necking through DIC measurements. This detection method was inspired by a physical understanding and experimental observations of the necking phenomenon. The method eliminates the derivative calculation from the traditional method, while it can directly determine the onset of localized necking through strain evolution curves. The robustness and accuracy of the method are also investigated through experiments. Imperfection and non-defect analyses, based on non-associated and associated flow rules, were utilized and compared to the determined results. The detection method provides satisfactory forming limit results and can be used as an alternative method to determine the forming limit diagram (FLD).