An extended Marciniak–Kuczynski model for anisotropic sheet subjected to monotonic strain paths with through-thickness shear

Abstract

Some metal sheet forming processes may induce an amount of plastic shear over the sheet thickness. This paper investigates how formability of anisotropic sheet metal is affected by such through-thickness shear (TTS). The Marciniak–Kuczynski (MK) model framework, a commonly used analytical tool to predict the limit of sheet formability due to the onset of localized necking, is extended in this paper in order to explicitly account for TTS in anisotropic metal sheets. It is a continuation of previous work by the present authors ( Eyckens et al., 2009), in which TTS is incorporated for isotropic sheet. This is achieved by the introduction of additional force equilibrium and geometric compatibility equations that govern the connection between matrix and groove in the MK model. Furthermore, in order to integrate plastic anisotropy, a material reference frame available in recent literature is incorporated, as well as a particular model for anisotropic yielding that relies on virtual testing of anisotropic properties (Facet plastic potential), since out-of-plane anisotropy related to TTS cannot be measured experimentally. It is found that formability may be increased by TTS, depending on the direction onto which it is imposed by the forming process. TTS is thus a relevant aspect of the formability in, for instance, sheet forming processes in which sliding contact with friction between sheets and forming tools occur.