Two topics, i.e., the scale effects and the geodesics of random heterogeneous materials will be discussed in this work. / When the separation of scales in random media does not hold, the representative volume element (RVE) of deterministic continuum mechanics does not exist in the conventional sense, and new concepts and approaches are needed. This subject is discussed here in the context of microstructures of two types - planar random chessboards, and planar random inclusion-matrix composites -- with microscale behavior being elastic-plastic-hardening (power-law). The microstructure is assumed to be spatially homogeneous and ergodic. Principal issues under consideration are those of yield and incipient plastic flow of statistical volume elements (SVE) on mesoscales, and the scaling trend of SVE to the RVE response on macroscale. Indeed, the SVE responses under uniform displacement (or traction) boundary conditions bound from above (respectively, below) the RVE response, and we show via extensive simulations in plane stress that the larger is the mesoscale, the tighter are both bounds. However, the mesoscale flows under both kinds of loading do not, in general, display normality. Also, with the limitation imposed by currently available computational resources, we do not recover normality (or even a trend towards it) when studying the largest possible SVE domains. / The second topic is the geodesic (i.e., shortest path) character of strain fields occurring in elasto-plastic response of planar inclusion-matrix composites. The composites' spatially random morphology is created by generating the disk centers through a sequential inhibition process based on a poisson point field in plane. Both phases (inclusions and matrix) are elastic-plastic-hardening with the matrix being more compliant and weaker than the inclusions, and perfect bonding everywhere. A quantitative comparison of a response pattern obtained by computational micromechanics with that found only by mathematical morphology indicates that (i) the regions of plastic flow are very close to geodesics, and (ii) a purely geometric, and orders of magnitude more rapid than by computational mechanics assessment of these regions is possible.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references. Also available in electronic version. Access restricted to campus users.

Ni/TiC metal matrix composites have been processed using the laser engineered net shaping (LENS) process. As nickel does not form an equilibrium carbide phase, addition of a strong carbide former in the form of titanium reinforces the nickel matrix resulting in a promising hybrid material for both surface engineering as well as high temperature structural applications. Changing the relative amounts of titanium and carbon in the nickel matrix, relatively low volume fraction of refined homogeneously distributed carbide precipitates, formation of in-situ carbide precipitates and the microstructural changes are investigated. The composites have been characterized in detail using x-ray diffraction, scanning electron microscopy (including energy dispersive spectroscopy (XEDS) mapping and electron backscatter diffraction (EBSD)), Auger electron spectroscopy, and transmission (including high resolution) electron microscopy. Both primary and eutectic titanium carbides, observed in this composite, exhibited the fcc-TiC structure (NaCl-type). Details of the orientation relationship between Ni and TiC have been studied using SEM-EBSD and high resolution TEM. The results of micro-hardness and tribology tests indicate that these composites have a relatively high hardness and a steady-state friction coefficient of ~0.5, both of which are improvements in comparison to LENS deposited pure Ni.