Plastic instability for off-axes loading in deep-drawing operations

International audienceThe aim of this study is the theoretical determination of the stress states at the onset of plastic instability for off-axes loading on an orthotropic sheet material. Marciniak and Kuczinskys' instability model has been developed wheere the principal-strain directions are not overlaid with the orthotropy directions, i.e. the rolling and transverse directions in both zones. According to the large-strains theory, this model includes the rotation of the anisotropy directions during the straining in both areas of the model. The computation is carried out for various orientations (0°, 30°, 45°, 60° and 90°) of the principal-strains directions from the principal orthotropy axes. The computed results so obtained are compared to those given by means of a step-by-step plastic calculation carried out along experimental strain paths determined using Marciniak punch. In every case, the results obtained from the two methods are almost completely similar. For the material studied (a mild steel for deep drawing), it is observed that the off-axes forming-limit stress diagrams at 30°, 45° and 60° are very close together and located above the in-axes stress curves (0° and 90°). Analysis of the influence of Lankfords' coefficients (r0, r45, r90) shows clearly that this property is a characteristic of the material studied and that for some other distributions of the anisotropy coefficients, the in-axes forming-limit stress diagrams may be distant from each other. A method is then proposed for using these forming-limit stress diagrams for the various directions of the sheet surface for necking prediction at the time of the numerical simulation of the deep-drawing operation by means of the finite-element method