Changes of Shape and Stress Distribution during Free-Bulging in Axi-Symmetrically Blow-Formed Superplastic Sheet

摘要

Changes of the shape and stress distribution during free-bulging in axi-symmetrically blow-formed super-plastic sheet are analyzed. Usually, the shape has been assumed to be a spherical surface while the stress distribution has been assumed to be a function satisfying only boundary conditions without any theoretical bases, because of nonlinear constitutive equations of superplasticity. An assumed stress distribution function gives a peculiar pressure to radius position of the workpiece. If the pressure distribution is uniform, it is proved that the function represents the true distribution of the workpiece. If the pressure distribution is uniform, it is proved that the function represents the true distribution of stress. Such a function is proposed in this paper and is also verified by the analysis without these surplus assumptions. With progress of forming, all areas except in the neighborhood of the periphery approach the equi-biaxial tensile stress state and the entire shape approaches that of a semi-sphere.