The development of a groove on the surface of a polycrystal where it is intersected by a grain boundary is governed by a fourth-order non-linear partial differential equation. Solutions have been found previously for isotropic and theoretical liquid crystal materials. It was hoped further materials could be modelled using constitutive functions derived from symmetry classification techniques. It was found, however, that only a reduction to third order was possible by finding the point symmetries. Furthermore, higher order terms remained in the boundary conditions.
- Grooving of a Bicrystal – Introduction
- Grooving of a Bicrystal – Derivation of the Evolution Equation
- Grooving of a Bicrystal – Isotropic Materials
- Grooving of a Bicrystal – New Constitutive Functions
- Grooving of a Bicrystal – Symmetry Reductions
- Grooving of a Bicrystal – Symmetric Grain Boundary Groove Problem
- Grooving of a Bicrystal – Conclusions
- Grooving of a Bicrystal – Bibliography
This was my project for the Master of Mathematics undertaken at the University of Wollongong. It was submitted in 1997. My supervisor was Dr Peter Tritscher.
© Andrew Wright, 1997, 1999