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

| PDF 413Kb |

Official URL: http://imamat.oxfordjournals.org/cgi/content/abstr...

## 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 |

Repository Staff Only: item control page