| The spatial distribution of second-phase particles in materials, and inhomogeneities such as clusters of second-phase particles, are known to affect bulk properties of particle-containing materials. The lack of a convenient method for quantitative characterization of the spatial distribution of second-phase particles has limited understanding of the mechanisms underlying these effects. The Dirichlet tessellation, and the associated dual tessellation, provide a unique, geometrical description of the spatial distribution of second-phase particles. This dissertation describes a computerized analysis, based on the Dirichlet tessellation, for quantitative characterization of the spatial distribution of second-phase particles. The analysis was designed to operate on a PC in the interest of wide applicability. For reasons of computational simplicity, particle size and morphology are excluded from the analysis. The analysis provides statistical descriptions of several microstructural variables, including local particle density and nearest-neighbor distances. An analysis of particle clustering, based on the dual tessellation and an assumed particle interaction distance, provides a detailed description of clustering of second-phase particles. Analysis of computer-generated particle distributions provides insight into the effect of spatial inhomogeneities and plane-strain deformation on the tessellation and clustering characteristics of various types of particle distributions. The analysis method was applied to determining the effects of type and degree of deformation processing on the spatial distribution of oxide fragments in PM-Al alloy sheet. Forging with subsequent rolling, and cross-rolling, were found to produce significantly more effective fragmentation and dispersal of the oxide skin than direct-rolling, per unit effective strain. The effect of deformation on clustering characteristics of oxide fragments in direct-rolled sheet exhibits good agreement with results from simulations using computer-generated particle arrays. |
