LIMITS TO THE DUCTILITY OF METAL SHEETS SUBJECTED TO COMPLEX STRAIN-PATHS

Localized necking in sheets under biaxial tension is analysed by using a Marciniak-Kuczynski localization approach along with a new plane-st ress yield criterion. The determination of the forming limits under li near, bilinear and curvilinear strain-paths, shows that a simple effec tive 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 propos ed, for either positive or negative values of the strain-rate ratio. T hese expressions are then implemented in finite element simulations of sheet-metal forming processes, so as to be used as a detector of neck ing. The pertinence of this approach is discussed in the case of the h emispherical punch test and of the cup drawing test. (C) 1998 Elsevier Science Ltd. All rights reserved.