General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

Abstract

A mathematical representation of the transformation of an orientation function between two sets of Cartesian coordinates is discussed in terms of a series expansion of the distribution function in generalized spherical harmonics. A general procedure for calculating the mechanical anisotropy of a single‐phase system (a polycrystalline material) from the orientation of its structural units and the intrinsic mechanical anisotropy of the structural unit is discussed in relation to the transformation of the orientation distribution function, i.e., mutual conversion of the coefficients in the expansion of the distribution function between the two sets of Cartesian coordinates. The procedure is extended to a two‐phase systems (semicrystalline polymers) containing structural units composed of crystalline and noncrystalline materials in three different geometrical arrangements.