## Vacuum moulding of a superplastic in two dimensions

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S J Chapman, A D Fitt
& G C PULOS

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