Abstract
The complete form of the fundamental equation of quantitative microstructural analysis of multiphase aggregates is formulated and presented. Six new theorems are derived and combined with earlier work by Delesse, Rosiwal and Thompson to form the overall fundamental equation. It is shown that the volume fraction of any constituent phase in a uniform multiphase aggregate with a random-curvature surface is exactly equal to its areal, lineal, or point fractions, measured either on the randomly curved surface of the solid; on its surface-projected normal image; or averaged over planar sections of the multiphase aggregate. It is found that the fundamental equation applies equally well to common solids with geometrical symmetry (polyhedral, spherical and cylindrical solids) provided the phase of interest is of uniform distribution, and that such solids are sampled from the parent matrix at random. The proposed theory can be used for the determination of spacial phase distribution of non-uniform multiphase aggregates. Several applications of the fundamental equation to quantitative fractographic analysis are also discussed with emphasis on plane-strain void fracture in ductile materials.
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