SUPERPLASTIC SHEET-METAL FORMING OF A GENERALIZED CUP .2. NONUNIFORM THINNING

A computational process model for the superplastic formation of a generalized cup is presented that takes into account the variation in thinning in the unsupported region. The relative pole to edge thinning arises due to the change in the state of stress from balanced biaxial at the pole to plane strain at the edge. Using kinematic conditions and material constitutive equations, a relationship between the instantaneous thickness at the pole and edge is developed. An equation for thickness variation from center to edge in terms of convected coordinates is postulated. Process parameters including thickness profile and pressure-time cycle for the generalized cup are determined using an incremental formulation. The solution developed in Part II depends on process and material parameters, unlike the uniform thinning model. The thickness profile for different shapes like the dome, cup, and cone formed from superplastic aluminum 7475 and aluminum-lithium alloys are compared with experimental results.