Obtaining the dimensions and orientation of 2D rectangular flakes from sectioning experiments in flake composites

Recently, we developed and reported the statistical validity of two methods for determining the planar aspect ratios of two-dimensional (2D) rectangular flakes in composites from the statistics of intersection lengths: one method is based on the maximum intersection length and the other on the average intersection length. In this work, we show that these methods are valid and robust not only for flakes having isotropic, random in-plane orientations but for the more general situations of planar orientations ranging from unidirectional (misalignment angle ε = 0), to partially aligned (0< ε < π/2), to flakes of isotropic, random-in-plane orientations (ε = π/2). We prove, by Monte Carlo simulations and by numerical sectioning experiments, the validity of the proposed methods for characterizing the extent of the partial alignment (the misalignment angle ε) of 2D rectangular flakes in composites, based again on the statistics of the intersection lengths; this information can be obtained from cross-sections of composite samples used in optical or electron microscopy or using tomographic imaging techniques. The performance of these techniques was tested using blind experiments in numerically sectioned composites, which contained up to 10⁶ individual flakes, and was found to be very good for a wide range of flake aspect ratios.