<p> This thesis details work done in the development of the phase field model which
allows simulation of elasticity with diffuse interfaces and the extension of a thin
interface analysis developed by previous authors to study non-dilute ideal alloys.
These models are coupled with a new finite difference adaptive mesh algorithm to
efficiently simulate a variety of physical systems. The finite difference adaptive
mesh algorithm is shown to be at worse 4-5 times faster than an equivalent finite element
method on a per node basis. In addition to this increase in speed for explicit
solvers in the code, an iterative solver used to compute elastic fields is found to
converge in O(N) time for a dynamically growing precipitate, where N is the number
of nodes on the adaptive mesh. A previous phase field formulation is extended
such as to make possible the study of non-ideal binary alloys with complex phase
diagrams. A phase field model is also derived for a free energy that incorporates an
elastic free energy and is used to investigate the competitive development of solid
state structures in which the kinetic transfer rate of atoms from the parent phase
to the precipitate phase is large. This results in the growth of solid state dendrites.
The morphological effects of competing surface anisotropy and anisotropy in the
elastic modulus tensor is analyzed. It is shown that the transition from surfaceenergy
driven dendrites to elastically driven dendrites depends on the magnitudes
of the surface energy anisotropy coefficient (E4 ) and the anisotropy of the elastic
tensor (β) as well as on the super saturation of the particle and therefore to a specific
Mullins-Sekerka onset radius. The transition point of this competitive process
is predicted from these three controlling parameters. </p> / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19732 |
| Date | 11 1900 |
| Creators | Greenwood, Michael |
| Contributors | Provatas, Nikolas, Materials Science |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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