Comparing two measures of flake alignment

Summary

Alignment of particles in structural composites is desirable to increase the strength and stiffness of the panel in one direction. The magnitude of resulting orthotropic panel properties are influenced by the degree of alignment. Quantification of the degree of alignment in the literature has primarily been attained by a parameter known as percent alignment. Measures of flake alignment in probability distribution form have received some, though more limited attention. However, use of statistical distributions to describes particle orientation, such as that provided by the von Mises distribution are needed for simulations of composite panel properties. It is shown that percent flake alignment is a linear transformation of the first moment (arithmetic mean) of the absolute value of angles in the range ±90 degrees. Assuming the von Mises distributional form accurately measures flake alignment, this implies that percent flake alignment is a measure of both the variability in flake direction and the mean flake angle. The numerical relationship of percent alignment with mean angle and variability is presented with a look-up table provided for converting between the two systems of measure. The relation will permit verification of models which employ the von Mises distribution to describe flake alignment using information in the literature based on percent flake alignment. A computer program is available from the author which will calculate percent alignment and distribution parameters for an experimentally obtained samples of angles.