MICROSTRUCTURAL SHAPE FACTORS - RELATION OF RANDOM PLANAR SECTIONS TO3-DIMENSIONAL MICROSTRUCTURES

The relation of random planar sections of anisometric microstructures to the actual three-dimensional anisometric is considered for oblate a nd prolate spheroids and cylinders. Simple formulae are obtained relat ing the two-dimensional (2-D) to three-dimensional (3-D) aspect ratios ; for oblate systems with large aspect ratios, the area-weighted avera ge 2-D aspect ratio varies linearly with the actual aspect ratio, wher eas for prolate systems of large aspect ratio, the 2-D aspect ratio va ries logarithmically with actual aspect ratio. Extension to polydisper se systems yields a shape factor, R, which gives greatest weight to gr ains (or particles) having the highest volume fraction. This not only preserves the linear and logarithmic functionalities found in monodisp erse systems, but favorably affects the sensitivity of R to visually a pparent differences among microstructures.