Necking in sheet metal forming. Influence of macroscopic and microscopic properties of materials

The necking of sheet metal is a main problem in forming processes that causes unacceptable thickness decreasing and leads to stop the process. There is a large amount of literature and research papers in this field. But the remaining problems to solve are the applicability and the accuracy of the methods for determining forming limits for various strain paths encountered in industrial processes. In the paper, we demonstrate that the linear stability analysis can provide accurate results considering various constitutive relationships and also considering that now the finite element analyses provide accurate results concerning the main field variables. The method is first presented, and then developments are done in the rigid-plastic case or in the rigid-plastic one accounting for damage by void growth. It is then demonstrated that the proposed method gives accurate results and then can be substituted to classical forming limit analyses.