Elastic properties of pyrolytic carbon with axisymmetric textures

Abstract

In this paper, the first-order bounds, the geometric mean, the singular approximation and the self-consistent estimate of the linear elastic properties of pyrolytic carbon (PyC) are determined numerically. The texture, i.e. the orientation distribution of the normal direction of the graphene planes, is modeled by a Fisher distribution on the unit sphere. Fisher distributions depend only on one scalar concentration parameter. It is shown in detail how the effective elasticities of PyC can be estimated based on the one concentration parameter which describes the scatter width of the orientation distribution. The numerical predictions of the different bounds and estimates are compared.