中文摘要：

成形极限图是一种评估单向拉伸到双向等拉应力范围内板料成形性能的有效手段。传统板料成形中，法向受到的应力远小于面内应力，所以，传统成形极限图是基于忽略法向应力而简化为平面应力状态的理论计算。该文论述了传统成形极限图以及现有的考虑法向应力影响的二维成形极限图在研究液压成形中流体压力影响时存在的缺陷与不足；同时，在二维成形极限图以及固体现实应力空间的基础上，建立了以法向流体压力 p的函数 f （p）为第三轴的三维成形极限图。该三维成形极限图不仅可以考虑液压成形中流体压力的影响，而且能够形象直观呈现出成形极限随流体压力的变化速率。

英文摘要：

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 theo-retical 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-di-mensional FLD was established based on the two-dimensional FLD and the real stress space of solid .The third axis of the three-di-mensional 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 .