Effect of plastic anisotropy on the prediction of the ductility for HCP sheet metals

Due to their lightness, low stiffness and high strength, Hexagonal Closed Packed (HCP) materials are widely used in aeronautic and aerospace industries. In this paper, the ductility limit of HCP sheet materials at room temperature (25° C) is predicted by coupling the Cazacu yield function and the Marciniak and Kuczynski (MK) necking criterion. Based on transformed principal stresses, the phenomenological constitutive model of Cazacu is used to take into account the initial plastic anisotropy and strength differential (SD) effects. For plane stress and orthotropic symmetry, two linear transformations are required to use a number of anisotropy coefficients which are more suitable for practical applications. Under these circumstances, a prediction of formability for HCP sheet materials with more than one linear transformation is performed using the numerical tool Mathematica.