One-dimensional tensile constitutive equation cannot be directly generalized to deal with two-dimensional bulging mechanical problems

Superplastic forming has been extensively applied to manufacture parts and components with complex shapes or high-precisions. However, superplastic formation is in multi-stress state. In a long time, uniaxial tensile constitutive equation has been directly generalized to deal with multi-stress state. Whether so doing is feasible or not needs to be proved in theory. This paper first summarizes the establishing processes of superplastic tensile and bulging constitutive equation with variable m, and, using the analytical expressions of equivalent stress a and equivalent strain rate e of free bulge based on the fundamentals of continuum medium plastic mechanics, derives the analytical expressions of optimum loading rules for superplastic free bulge. By comparing the quantitative results on typical superplastic alloy ZnAI22, it is shown that one-dimensional tensile constitutive equations cannot be directly generalized to deal with two-dimensional bulging quantitative mechanical problems; only superplastic bulging constitutive equation based on bulging stress state can be used to treat the quantitative mechanical problems of bulge.