Bivariate stereological unfolding procedure for randomly oriented chopped fibers or whiskers

The microstructural characterization of randomly oriented, polydisperse chopped fiber or whisker composites is considered. A method of unfolding fiber length distributions from the distribution of section sizes created on a polished sectioning is derived, and a general equation relating two-dimensional and three-dimensional distributions is presented. The univariate unfolding of length distributions is shown to be applicable to bivariate length-diameter unfolding problems through an iterative application of the univariate technique. This stereological unfolding procedure has been applied to a discontinuously reinforced titanium alloy matrix composite for the estimation of the threedimensional bivariate size and shape distribution of TiB whiskers.