Marciniak–Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal

The Marciniak–Kuczynski (MK) forming limit model is extended in order to predict localized necking in sheet metal forming operations in which Through-Thickness Shear (TTS), also known as out-of-plane shear, occurs. An example of such a forming operation is Single Point Incremental Forming. The Forming Limit Diagram (FLD) of a purely plastic, isotropic hardening material with von Mises yield locus is discussed, for monotonic deformation paths that include TTS. If TTS is present in the plane containing the critical groove direction in the MK model, it is seen that formability is increased for all in-plane strain modes, except equibiaxial stretching. The increase in formability due to TTS is explained through a detailed study of some selected deformation modes. The underlying mechanism is a change of the stress mode in the groove that results in a delay of the onset of localized necking.