The Mathematical Institute, University of Oxford, Eprints Archive

Vacuum moulding of a superplastic in two dimensions

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

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Abstract

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.

Item Type:Article
Subjects:H - N > Mechanics of deformable solids
O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:596
Deposited By:Jon Chapman
Deposited On:18 May 2007
Last Modified:20 Jul 2009 14:22

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