Archive of Applied Mechanics

, Volume 84, Issue 1, pp 133–148 | Cite as

Micromechanical estimate of the elastic properties of the coherent domains in pyrolytic carbon

  • S. Lin
  • T.-A. Langhoff
  • T. Böhlke


On the nanoscale, the microstructure of pyrolytic carbon (PyC) is constituted by an ensemble of graphene planes, which manifest themselves as lattice fringes in high-resolution transmission electron microscope images. This microstructure can be also considered by an aggregate of so-called coherent domains consisting of stacks of graphene planes with a common unit normal vector. In order to homogenize the elastic behavior of PyC on the micro-level, image processing techniques are used to detect the coherent domains. Subsequently, the domain orientation distribution function (DODF) is modeled by means of a von Mises-Fisher distribution. The main objective of the present paper is to estimate the elastic properties of the coherent domains of the PyC microstructure. Moreover, the Hashin-Shtrikman bounds for the elastic properties can be determined by taking into account the DODF and by applying a nonlinear averaging procedure of the spatially dependent deviations of the local elastic properties. The elastic properties of the coherent domains are estimated by an inverse parameter identification of the Hashin-Shtrikman homogenization method by using effective elastic properties. The latter ones have been obtained based on an Fourier-based image processing algorithm and the orientation distribution function of the graphene planes in a recent paper (Böhlke et al. in Z Angew Math Mech, 2012).


Pyrolytic carbon Coherent domains Elastic properties Homogenization Image processing 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Chair for Continuum Mechanics, Department of Mechanical Engineering, Institute of Engineering MechanicsKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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