Chapman, S. J. (1999) Vacuum moulding of a superplastic in two dimensions. IMA Journal of Applied Mathematics, 63 (3). pp. 217-246. ISSN 1464-3634
Official URL: http://imamat.oxfordjournals.org/cgi/content/abstr...
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.
|Subjects:||H - N > Mechanics of deformable solids|
O - Z > Partial differential equations
|Research Groups:||Oxford Centre for Industrial and Applied Mathematics|
|Deposited By:||Jon Chapman|
|Deposited On:||18 May 2007|
|Last Modified:||20 Jul 2009 14:22|
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