The Prediction of Necking and Failure in 3 D. Sheet Forming Analysis Using Damage Variable

Abstract
The modeling of necking occurrence in sheet metal forming is a real challenge for the engineer concerned with processing of new geometries and materials. As fracture in metal forming is mainly due to the development of ductile damage and to represent the failure of anisotropic sheet-metals, an extension of the Gurson-Tvergaard model is presented and implemented in the context of plane-stress for shell elements. A one dimensional problem is solved and compared with the exact solution of the literature. The paper closes with a numerical and experimental study of the necking of a square cup deepdrawing using the modified Gurson's model to described the constitutive behavior of the material. Finally, a numerical necking criterion is proposed.