SUPERPLASTIC SHEET-METAL FORMING OF A GENERALIZED CUP .1. UNIFORM THINNING

Superplasticity is the phenomenon observed in certain materials that deform on the order of 300 to 500% under very low now stress, high temperature, and fine grain structure. Superplastically formed parts find application as both structural and nonstructural components in simple and complex shapes. Mathematical models that describe the forming process with optimum strain rate and tool geometry as input and pressure-time and thickness as output are essential for successful forming. This article describes the deformation of a generalized cup assuming uniform thinning in the unsupported region. Closed form equations are developed relating process parameters like pressure-time loading and thickness distribution to the shape of the cup and material properties. The generalized cup formulation is applicable to the superplastic forming of domes, right circular cylinders, deep slanted cups, and cones.