  Three-scale homogenization procedure is proposed in this paper to provide
estimates of the effective thermal conductivities of porous carbon-carbon
textile composites. On each scale - the level of fiber tow (micro-scale), the
level of yarns (meso-scale) and the level of laminate (macro-scale) - a two
step homogenization procedure based on the Mori-Tanaka averaging scheme is
adopted. This involves evaluation of the effective properties first in the
absence of pores. In the next step, an ellipsoidal pore is introduced into a
new, generally orthotropic, matrix to make provision for the presence of crimp
voids and transverse and delamination cracks resulting from the thermal
transformation of a polymeric precursor into the carbon matrix. Other sources
of imperfections also attributed to the manufacturing processes, including
non-uniform texture of the reinforcements, are taken into consideration through
the histograms of inclination angles measured along the fiber tow path together
with a particular shape of the equivalent ellipsoidal inclusion. The analysis
shows that a reasonable agreement of the numerical predictions with
experimental measurements can be achieved.
