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 three-dimensional bivariate size and shape distribution of TiB whiskers.