Equal channel angular extrusion (ECAE) has attracted a substantial attention for it provides the opportunity to introduce large plastic strain into the material in the bulk form. Both die angles and processing routes have been recognized as the important parameters in applying ECAE to fabricate ultrafine-grained materials. Unfortunately, studies of different group provided inconsistent conclusions on the effectiveness of processing routes, which are believed to be due to the incomplete microstructural information obtained in each investigation. In the present work, quantitative analysis of the microstructure developed by different processing conditions were conducted using transmission electron microscopy (TEM), in which the morphology, size, and shape of subgrains as well as boundary misorientation were fully characterized. A commercial pure aluminum (AA 1050) was deformed by ECAE to strain of ~ 8 with different routes (A, Bc and C, in terms of reorientation angle 0o, 90o, and 180o respectively of the billet between two extrusion passes) and die angles. The results show that the effectiveness of high angle boundary (HAB) formation is in the sequence of route A¡ÜBc>C. However, in terms of grain refinement, the effectiveness is in the order of route Bc>A>C. In addition, route A produces subgrains with the most elongated shape, while route Bc produces subgrains with the most equiaxed shape. These results may be attributed to the different shear pattern introduced in each route. ECAE die angle determines both the strain per pass and the shear plane orientation. In route C, the shear is maintained in the same plane and the effect of strain per pass can be studied. With route C, both the 90o and 120o die produce microstructure with similar HAB proportions, but they result in different arrangement of HABs. The 120o die produces subgrains with larger size and higher aspect ratio than the 90o die does in route C. Generally speaking, for the die angle range studied, the different values of strain per pass used in ECAE mainly affect the morphology of the subgrains. On the other hand, the effect of die angle is weakened with route Bc as compared to route C, which may be attributed to the intersection of shear planes involved in route Bc.

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A method for the retrieval of grain boundary inclination parameters of the grain boundary character distribution by oblique double-sectioning is proposed. The method, which is similar to the recovery of the orientation distributions from sets of incomplete pole-figures, is described along with a framework for implementation. The method directly measures grain boundary inclinations in a manner similar to serial sectioning while statistically sampling the microstructure comparably to stereological methods. Computer simulations of the method were used to confirm the mathematical framework. Additional simulations, where the grain boundary normal distributions were recovered by both oblique double-sectioning and stereological methods, showed that results recovered by 3 orthogonal double-sections from oblique double-sectioning proved to be just as accurate as the 25 section-cuts required for stereology in resolving the finer details in the recovered distribution.

[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.