Vacuum moulding of a superplastic in two dimensions

A mathematical model is proposed for the process of vacuum superplastic for ming. The model exploits the fact that in most industrial applications the sheet aspect ratio (thickness/sheet width) is small. After an initial consi deration of some of the more general properties and the literature of super plastic materials, the elastic/plastic deformation of an internally-inflate d thin-walled cylinder is examined. Plates of arbitrary geometry are then c onsidered. A quasisteady model in which the sheet moves through a sequence of steady states is developed. Some simplified closed-form solutions are ex amined, but for general cases a system of nonlinear partial differential eq uations must be solved numerically. An efficient and accurate semi-explicit numerical scheme is proposed and a simplified stability analysis is presen ted; the method is then used to compute properties of superplastic vacuum m oulded sheets in a number of practically motivated cases.