Mathematical models for the glass sheet redraw process

Thesis

In this thesis we derive mathematical models for the glass sheet redraw process for the production of very thin glass sheets. In the redraw process, a prefabricated glass block is fed into a furnace, where it is heated and stretched by the application of draw rollers to reduce its thickness. Redrawn sheets may be used in various applications including smartphone and battery technology. Our aims are to investigate the factors determining the final thickness profile of a glass sheet produced by this process, as well as the growth of out-of-plane deformations in the sheet during redraw. Our method is to model the glass sheet using Navier–Stokes equations and free-surface conditions, and exploit small aspect ratios in the sheet to simplify and solve these equations using asymptotic expansions.

We first consider a simple two-dimensional sheet to determine which physical effects should be taken into account in modelling the redraw process. Next, we derive a mathematical model for redraw of a thin threedimensional sheet. We consider the limits in which the heater zone is either short or long compared with the sheet half-width. The resulting reduced models predict the thickness profile of the redrawn sheet and the initial shape required to redraw a product of uniform thickness. We then derive mathematical models for buckling of thin viscous sheets during redraw. For buckling of a two-dimensional glass sheet due to gravity-induced compression, we predict the evolution of the centreline and investigate the early- and late-time behaviour of the system. For a three-dimensional glass sheet undergoing redraw, we use numerical solutions to investigate the behaviour of the sheet mid-surface.

Authors: O'Kiely, D

• DOI: 10.5287/ora-azpooyqqr
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Keywords: industrial mathematics; glass; asymptotics; mathematical modelling; thin viscous sheet