Three-dimensional forming limit diagram for fluid pressure forming of tubes

Forming limit diagram (FLD) is an effective means usually used to access sheet metal formability from uniaxial tension to biaxial equal stretching state. In the conventional sheet metal forming process, the through thickness normal stress is far less than the in-plane stresses, so the through thickness normal stress can be ignored and the plane stress state is adopted for the theoretical calculation of FLD. In this paper, the limitations of using conventional FLD and two-dimensional FLD considering the effect of through thickness normal stress in studying the fluid pressure effect in hydroforming were discussed. Then the three-dimensional FLD was established based on the two-dimensional FLD and the real stress space of solid. The third axis of the three-dimensional FLD was represented by f (p) which is a function of the fluid pressure. The three-dimensional FLD not only can be used to investigate the effect of the fluid pressure in hydroforming, but also used to express the variation rate of the forming limit along with the increasing of the fluid pressure.