Investigation of the Dislocation Slip Assumption on Formability of BCC Sheet Metals

Abstract

It is well known that the yield-surface shape greatly affects the prediction of strain-limit values, especially for biaxial-stretching paths. The sharpness of the material yield surface (PCYS) is related to the slip systems selected to accommodate the imposed deformation. Polycrystal models track the slip activity of each individual grain, allowing the evolution of anisotropy to be taken into account naturally. Consequently, we can correlate the change in the yield surface to the number and relative activity of the active slip systems.
In this study, we focus on how different plastic crystal-anisotropy assumptions influence the predicted formability strains. The forming-limit diagrams (FLDs) are calculated based on a ratedependent polycrystal model together with the Marciniak-Kuczynski (M-K) approach, which develops localized necking from an initial imperfection in the form of a narrow zone across the sheet.
Typically, numerical simulations of the FLDs performed for BCC sheets assume either 24 slip systems, of the type {110}<111> and {112}<111>, or 48 slip systems, also including {123} slip planes. Because the essential characteristics of multiple glide can be captured using 24 or 48 slip systems, researchers have been free to select either of the deformation modes for crystal plasticity simulations. However, when predicting FLD behavior with the full-constrain (FC) homogenization scheme, the selection of the active deformation modes strongly affects the calculated limit strains. For example, if two deformation modes are selected, the MK-FC model predicts unrealistically high limit strains in balanced-biaxial tension. These different behaviors can be avoided if a self-consistent (SC) homogenization scheme is used instead of the classical FC approach. The discrepancy between the MK-FC and MK-SC assumptions can be understood in terms of the differences in the slip systems selected by each case and, consequently, in the predicted lattice rotation and local curvature of the yield locus.