Estimate of the Domain Orientation Distribution Function and the Thermoelastic Properties of Pyrolytic Carbon Based on an Image Processing Technique

The microstructure of Pyrolytic Carbon (PyC) can be described as an aggregate of coherent domains with different orientations. The domains exhibit an approximately a hexagonal material symmetry. In order to apply statistical homogenization schemes which predict the thermomechanical properties in terms of the microstructural characteristics, a quantitative description of PyC microstructures based on the domain orientation distribution function (DODF) is introduced in this work. The von-Mises Fisher distribution is applied for modeling the orientation of the unit normal vectors of the graphene planes. The respective probabilty density function depends on the so-called concentration parameter κ. The parameter κ is estimated by the set of domain orientations, which can be obtained by applying the image processing technique. This procedure facilitates the estimate of the 2nd order bounds (Hashin-Shtrikman upper and lower bounds) based on the real microstructure. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)