Homogenization of the elastic properties of pyrolytic carbon based on an image processing technique

In this work, the linear elastic material properties of differently textured variants of pyrolytic carbon are homogenized from the submicro- to the micro-scale. In high resolution transmission electron microscope (HRTEM) lattice fringe images, the microstructure of pyrolytic carbon manifests itself in terms of projections of graphene layers. According to their orientation distribution, different textures of pyrolytic carbon have been classified. Assuming a von Mises-Fisher distribution for the spatial orientation of single graphene layers, the orientation distribution function of the projected layers in the image plane is analytically found to be a modified Struve function. For each pyrolytic carbon texture, Maximum-likelihood estimates for the mean orientation and the concentration parameter of the von Mises-Fisher distribution are obtained numerically. Hereby, Fourier transformation and appropriate filters are used to determine the probabilities for discrete orientations of the graphene layers directly from HRTEM images. First- and second-order bounds of the linear elastic properties of pyrolytic carbon of the different textures are computed. Elastic constants of graphite and pyrolytic graphite have been used for modeling the elastic behavior of the graphene layers within a continuum mechanical setting. Due to the high anisotropy of all analyzed textures of pyrolytic carbon, the differences even between the second-order bounds are quite large.