Limits to the ductility of metal sheets subjected to complex strain-paths

Abstract

Abstract Localized necking in sheets under biaxial tension is analysed by using a Marciniak-Kuczynski localization approach along with a new plane-stress yield criterion. The determination of the forming limits under linear, bilinear and curvilinear strain-paths, shows that a simple effective strain approach defining the limit to ductility as a function of the current strain-rate ratio applies with good accuracy for arbitrary strain-paths. Analytical expressions of the forming limits are proposed, for either positive or negative values of the strain-rate ratio. These expressions are then implemented in finite element simulations of sheet-metal forming processes, so as to be used as a detector of necking. The pertinence of this approach is discussed in the case of the hemispherical punch test and of the cup drawing test.