On the stability of biaxial stretching with application to the optimization of superplastic blow-forming

The instability of biaxial stretching of thin sheets of viscoplastic metals under plane stress conditions is investigated using a linear stability analysis. An instability criterion for biaxial stretching is developed based on the assumption that localized necking initiates along the direction perpendicular to the major principal stress direction. Various ''optimum'' variable strain rate paths, which ensure a stable deformation of the sheet without neck formation, are computed for different strain ratios based on the instability analysis. The variable strain rate paths are applied in the finite element modeling of the superplastic uniaxial extension of a tabular specimen and superplastic blow-forming of a hemisphere. A reduction of forming time is achieved compared with the established constant strain rate forming method, while uniformity in the thickness distribution of the formed parts are maintained.