Abstract
Grain and pore morphologies are investigated in polycrystals which have an idealised microstructure. For such polycrystals pore behaviour and paths to grain growth are well defined due to the high degree of symmetry present. This is in contrast to. the intractable randomness generally observed in reality. Grain growth in non-porous structures is investigated in both two and three dimensions, Chapters 2 and 3 respectively. Two models in particular are considered. In the first growth is initiated by a single rogue grain either shrinking or growing in an otherwise uniform array of grains until an unstable configuration results. It is found that if the rogue grain shrinks the material can recrystallise into a uniform array of larger grains. If the rogue grain grows abnormal growth is expected to follow. In the second model growth in regular structures is considered. Such structures comprise n(n= 1,2,3) different types of grain which pack together in a regular way to fill space. Growth occurs because of instabilities arising from the different types of grain present and is assumed to occur in such a way that regularity, or homogeneity, throughout the material Is retained at all times. These models of grain growth developed here are entirely geometrical. Also in Chapter 2 we develop a model to investigate the effect of grain edge pore drag in' two-dimensional polycrystals. The expected qualitative behaviour is predicted. Chapter 4 is concerned with the stability and morphology of interlinked porosity in three-dimensional regular bimodal polycrystals. Here the material comprises two types of tetrakaidecahedra, large and small, enabling the effects of grain size variation on pore stability to be investigated. The results obtained here are interpreted with respect to the sintering of powder compacts and fission gas release which occurs during the irradiation of UO[2] nuclear fuel. It is found that during sintering interlinked porosity breaks down earlier than previously pre-dieted. It is also found that the fractional pore volume required to support an interconnected tunnel structure in UO2 during irradiation is almost insensitive to grain size variation. Both of these results are in good agreement with experimental observations. In Chapter 5 preliminary methods are developed to enable the results of Chapter 4, initially pertaining only to idealised materials, to be applied to materials with more realistic grain size distributions.